Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The game scenario schedules six lab sessions over three days, with one session each morning and each afternoon. Each session is led by one of six different lab assistants—J, K, L, N, O, and R. This combination of six assistants leading six different lab sessions creates a Balanced Advanced Linear setup:

PT66_J12_Game_#1_setup_diagram 1.png

As always, the choice of AM (morning) and PM (afternoon) for the top or bottom row is yours. The diagram does not change in any functional way if the AM row is on top and the PM row is on the bottom.

The first rule conveniently establishes a vertical block of K and R. Because the rule does not establish which assistant leads the morning or afternoon session, the block rotates:

PT66_J12_Game_#1_setup_diagram 2.png

Or, if you prefer to use one diagram to represent this block, a circle can be drawn around KR, in order to represent the rotation of the variables:

PT66_J12_Game_#1_setup_diagram 3.png

The rule does not assign a relative position to the KR block, and thus no Not Laws or restrictions follow from this rule.

The second rule initially seems innocuous, but it has a powerful effect on the game. This rule separates L and O, and forces them to lead sessions that meet on different days. By itself, this rule would typically just establish a vertical not-block, but, when the implications of the first rule are considered, this rule creates two separate blocks. Let’s examine how:

• There are only three separate days available for a lab assistant to lead a session. The KR block fully occupies one of those three days. Thus, when L and O are forced to lead sessions on different days, the following basic block lineup must exist (this is not a Linear order the variables must conform to; instead this is a Grouping arrangement, so the variable on the top or bottom is not relevant in this view):

PT66_J12_Game_#1_setup_diagram 4.png

• From this perspective, four of the six available spaces are taken, which leads to one of the power inferences of the game: J and N cannot lead sessions on the same day, and instead must lead sessions that meet on different days. In this case, they must lead sessions with either L or O:

PT66_J12_Game_#1_setup_diagram 5.png

Thus, the combination of the first two rules creates three separate blocks, with each of these blocks occupying one complete day of the schedule. And while at this point some uncertainty still exists—the linear order of the blocks, the morning/afternoon schedules, and the exact assignments of J and N—the third rule and especially the fourth rule limits these uncertainties further. Let us examine the fourth rule first, as it relates the blocks to each other in a powerful manner.

The fourth rule sequentially relates the J and O. O must lead a session on the same day as N or J, but when the fourth rule is considered, J cannot lead a session on the same day as O, and thus N must lead a session on the same day as O. Consequently, J must lead a session on the same day as L, and the JL block must meet earlier than the NO block:

PT66_J12_Game_#1_setup_diagram 6.png

Again, these blocks do not yet take into account the morning and afternoon aspect of this game.

Thus, at this point, the KR block can appear on any day. The JL block always appears earlier than the NO block, so JL appears on Wednesday or Thursday; the NO block appears on Thursday or Friday. While Not Laws could be drawn to reflect these sequential inferences, because the blocks themselves are so powerful, we will eschew showing the Not Laws.

The third rule assigns N to an afternoon session, and from our analysis of the blocks we can infer that O must then lead a morning session. Thus, with the morning/afternoon aspect considered, the three blocks appear as follows:

PT66_J12_Game_#1_setup_diagram 7.png

This lineup of blocks clearly limits the number of possibilities in the game, and so the decision could be made to show the three basic templates that exist (two with JL on Wednesday, and one with JL on Thursday). For reference purposes, here are the three templates:

Template #1: JL block on Wednesday, NO block on Thursday

PT66_J12_Game_#1_setup_diagram 8.png

Template #2: JL block on Wednesday, NO block on Friday

PT66_J12_Game_#1_setup_diagram 9.png

Template #3: JL block on Thursday, NO block on Friday

PT66_J12_Game_#1_setup_diagram 10.png

Because the relationship of the blocks themselves suggests these limitations inherently, many students chose not to take the time to diagram out the three basic templates, and instead proceeded to the questions and simply used the powerful initial information to attack the game. These students did equally well on this game, and thus this becomes a situation where the templates are not necessary to attack the game, but can be helpful. However, we will not refer to these templates while solving the game.

[Lsatcat]

I am having trouble figuring out how to best diagram the variables and rules for the first game in section 3 of the June 2012 LSAT, the lab sessions game.

Any suggestions or a sample diagram would be greatly appreciated.

Thank you!

[Ron Gore]

Hi Cat!

This is an Advanced Linear game, with Wednesday, Thursday and Friday as the base and morning/afternoon stacks. By combining the first and second rules, you get a strong inference that makes this a Limited Solution Set game, with three templates. While the templates are not necessary to complete the game in good shape, the most skilled setup will include them.

As you can imagine, explaining the setup in detail is a several-page process, and this forum is not the best medium for that type of diagramming. If possible, could you let me know were you ran into trouble with your setup, and whether the hints I've given help you past those rough spots? I'll be happy to discusses those specific issues with you, and we'll try to figure out where it is you are missing the inferences.

Thanks!

Ron

[srcline@noctrl.edu]

Hello

So I think that my set up is correct for this game but I wanted to double check. So I had:

W: _(morning) _ (afternoon)

Th:-(morning) _ (afternoon)

F:_(morning) _(afternoon)


Rules:
1. KR block
2. not block LO
3. N Afternoon
4. J>O

The only inferences that I got was that O cant be on Wednesday and J cant be on Friday. N cant obviously be in the morning, but Im not seeing the connection b/w the first and second rules. I understand that there going to be two templates b/c of the first rule.

Thankyou
Sarah

[Emily Haney-Caron]

Hi Sarah,

You're definitely missing a key inference here, regarding who has to be on the same day. We know K and R are on the same day, and we know L and O aren't. So, that leaves two more pairs, made up of L, O, N, and J. Based on what you know, can you figure out who will be paired with who? This will require you to combine rules 2, 3, and 4. I don't want to give it to you, because I know you can work through this one on your own and you'll get so much more out of it that way. See if you can puzzle it through! If not, give it a day or two and then come back to it. If you really can't get it, let us know, and we can help a bit more. Otherwise, post once you figure out the answer.

[starre]

Hi Emily,

I'm not understanding this either. I had the same setup as Sarah. Afterwards, I redid the questions writing out the setup for each answer choice with each question and was able to get the correct answers, but I don't have time to do that extent of work on test day. Looking back at the answers, I can see what pairs with what, but I can't see how to come to that conclusion during the setup (meaning without having to go through all the answer choices to see it). Is there another hint you could give?

Thank you,
Emily

[Clay Cooper]

Hi Emily,

Thanks for your question.

Let's look at it this way: there are six variables, each of which must be paired with another. When we find out that K must be paired with R, we have eliminated two of the six and are down to four that must be paired amongst themselves. So, let's consider the variables that could be, for instance, J's partner: N, O, or L. We are told that J must meet on an earlier day than O, so that also tells us that J cannot be paired with O. That leaves N and L. However, if we were to pair J with N, that would force L and O to be paired, which we know is against the rules.

Do you see the inference to be made here? I think approaching it this way is how a test-taker can make the key inference before reaching the questions.

I hope that helps!

[starre]

That makes so much more sense! Thank you!!