Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

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

This game was widely considered the most difficult game of this LSAT. The first challenging decision comes in choosing a base. One possible base is the four bicycles F, G, H, and J, and the other possible base is the four riders R, S, T, and Y. Regardless of the base, each will use the two days, and so there will be two rows or columns for each. Let’s take a look at each base, using a vertical setup:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_1.png

Each of these setups will allow you to solve the game successfully. How then, do you determine which base is the best? The first and easiest method is to look at the answer choices to see which base the test makers use. While question #13 uses the second base (bicycles), the remaining questions use the first base (riders). So, the majority of questions use the riders as the base. Second, are there any rules which would be easier to display using one of the bases? In this case, yes: the fourth rule can easily be shown on the first setup by using internal diagramming. That rule is less powerfully shown as a block in the second diagram, and thus we will use the first base for our setup.

Prior to analyzing the four rules, let’s take a moment to understand the impact of the conditions given in the game scenario. The scenario contains two “cleanup” rules: each rider tests only one bicycle per day, and all four bicycles are tested each day. Thus, beneficially, we have a 1-to-1 balanced scenario in play. However, the game scenario also states that “Each rider will then test a different one of the bicycles on the second day.” Thus, when a rider tests a bicycle on either day, he or she cannot test that same bicycle on the other day. We will represent this in the diagram with a double-not arrow:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_2.png

Let us examine each rule.

First Rule:

The first rule establishes that R cannot test F:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_3.png

Second Rule:

This rule eliminates Y from testing J:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_4.png

Third Rule:

This rule stipulates that T must test H on one of the days. Because of the condition in the game scenario that states each rider tests a different bike each day, this means that T must test H on exactly one of the days only:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_5.png

Fourth Rule:

The final rule establishes that the bicycle tested by Y on the first day must be the same as the bicycle tested by S on the second day. Because each rider tests exactly one bicycle each day, this causes a reversal of the rule, creating a double-arrow that can be shown internally on the diagram:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_6.png

At this point, most students stop diagramming and move to the questions. But, take a moment to consider the interaction of the third and fourth rules:

• Y and S always test the same bicycle on days 1 and 2, respectively. T must always inspect H on one of the days. Could Y and S test H on days 1 and 2, respectively? No, because if they did so, H would be tested on each day, and thus would not be available to T on either day. Thus, we can infer that Y cannot test H on day 1 and S cannot test H on day 2:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_7.png

This is a very powerful inference in the game, and with an H Not Law added to Y on day 1, we can see that Y on day 1 is restricted to F or G. Because of the effect of the fourth rule, S on day 2 is also restricted to F or G:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_8.png

At this point, the game is now far more restricted than before, and you could proceed to the questions. Alternatively, the presence of the F/G dual option on Y and S suggests that this game has a limited number of templates, especially when the third rule is considered. The combination of the F/G dual-option and the third rule leads to four basic templates:

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_9.png

powerscore_M12_T4_O2011_LG_explanations_game_3_diagram_10.png

Although the templates are not necessary to conquer this game, they help considerably.

[jzhang1992]

I am doing the game involving a 2-day study for a cycling magazine. The problem is I don't really understand how the 4 templates set up in the explanation work.

Since there are options for each rider in the templates, how do you know which one of the options to use?

[Jacques Lamothe]

Hey jzhang,

Each individual template is a diagram that we can fill out more than our main diagram by assuming an additional piece of information. In the explanation of this game, the additional piece of information that is assumed in the construction of a template is put next to the template number. So for example, template 1 would be the diagram you use if you know that "F is in YS" and "H is in T1." If instead "F is in YS" but "H is in T2," you would use template 2.

If you are asking, "how can I know which variable to use when the template indicates that a space is filled by one of 2 or more possible variables?," the short answer is that you don't know exactly which variable to use. So for example, we know that the R1 slot of the first template will be filled by J or G, but either could be placed there. A template doesn't necessarily give you the exact location of every variable. It just helps you to narrow down the range of possible variable placements.

I hope this explanation of how the templates in this game is helpful. If I was unclear or misunderstood your question, please let me know!

Jacques

[isoifer]

I am also a bit confused about the templates. I understand that we cannot know all the information. But for example on template 1, why is R-2 a blank spot? Why couldn't it possibly be H/G/J? Should we only list the options if there are only two possible assignments to a given slot?

[Adam Tyson]

When faced with three choices out of four variables, isoifer, we generally find it cleaner and simpler, especially in this forum, to leave that space blank, but it would be perfectly acceptable to put that "triple option" in that space as you suggested. I do that when I work through this game in person with a class or tutoring student, but it can get a bit crowded and confusing in this forum.

[isoifer]

That makes sense. I just wanted to check because knowing me, I tend to feel panicked particularly in Logic Games and want to make sure I know EXACTLY what can stay in and EXACTLY what can stay out so I don't accidentally draw any wrong conclusions. Hopefully with more practice I won't have to write down as much information/make such crowded diagrams.

[jackbenimble106]

Good morning,

Regarding the double-not arrow you have between Yuki on the first day and Seamus on the second day, my initial thought was that this was a mistaken reversal.

What I mean is, the first rule says Y1 S2 and your diagram implies S2 Y1.

Am I approaching this too much like a LR question?

Thanks!

[Tajadas]

Could someone explain the rationale behind using RYTS as the base, rather than FGHJ, assuming one is looking at the test for the first time? I used FGHJ because I thought there could be no simpler way to diagram the fourth rule as [YS], and I still think drawing [YS] is simplier than having to draw arrows within the inside of the model. It made doing the templates themselves much harder though-- I ended up with 6 instead of 4.

[Adam Tyson]

This is a rare game that can work either way Tajadas, and my preference happens to be using the bikes as the base for the exact reason you cited: it makes diagramming the YS rule much easier, just a simple block instead of those diagonal lines. Most games have one clearly superior choice for the base, but this game really does work either way and comes down mostly to a question of style and how it appeals to you.

[pbui5300]

Hello,

This was a tough game for me. I did not draw out the four templates and it took me almost 20 minutes to finish this game. I read your diagram above and did the game again using the four templates. The templates made this game 10 times easier. Do you have any tips on how to know which games we should draw the templates and which game we shouldn't? I did not know templates were the quicker way to solve this game than the "no template" way. One thing I noticed is that this game has more global questions than local so templates would be good here, but this is just my guess. Thank you!