Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Linear/Grouping Combination Game.

The game scenario establishes that a radio update consists of five reports: two of general interest (I, N), and three of local interest (S, T, W). Unfortunately, the scenario alone does not provide enough information to produce a workable setup. You must thoroughly examine the rules and understand both the Grouping and the Linear aspects of the game before proceeding to create your diagram.

The first two rules are particularly important in this respect. Essentially, our job is to figure out the order in which the five reports are presented within each of two separate segment groups—one with 3 reports, and the other with 2. Within each segment, the ordering is done by length, longest to shortest:

PT72_Game_#1_setup_diagram 1.png

Because the reports are ordered by length within each segment, the segments must be considered individually when determining report order. For instance, the longest report overall (N) could be the first report in either segment; similarly the shortest overall report (S) could be the last report in either segment.

Now that we have a solid grasp of how the game works from the scenario and the first two rules, let’s turn to the third rule:

• Local: min. 1 of (S T W 3) per segment

Since the second segment contains only two reports, but there are a total of 3 reports of local interest, there will always be at least one report of local interest in the first segment (by default). However, it is important to note that at least one of the reports in the second segment must be of local interest:

PT72_Game_#1_setup_diagram 2.png

The fourth rule establishes that N is always the longest of the five reports. Since the reports are ordered by length, N must always be the first report in its segment. This produces a Split Dual-Option for N, along with three corresponding Not Laws:

PT72_Game_#1_setup_diagram 3.png

The next rule states that S is the shortest of the five reports. As with the previous rule, this means that S must be the last report in its segment. This produces a Split Dual-Option for S, along with three additional Not Laws:

PT72_Game_#1_setup_diagram 4.png

The last rule establishes the following sequence:

• I W

We must be careful when inferring Not Laws from this rule, because—theoretically—I could be the last report of either segment, as long as it is not in the same segment as W. Likewise, it may be possible to place W in the beginning of either segment, as long as W and I are in different segments. Such placements are likely to restrict the game considerably, which is why it is worth examining the hypothetical solutions for each:

1. I is the last report in the first segment:

PT72_Game_#1_setup_diagram 5.png

2. I is the last report in the second segment:

PT72_Game_#1_setup_diagram 6.png

3. W is the first report in the first segment:

• If W were the first report in the first segment, then I would need to be in the second segment in compliance with the last rule. However, since N must be the first report in its segment, N would also end up in the second segment:

PT72_Game_#1_setup_diagram 7.png

• This would violate the third rule requiring that each segment contain at least one report of local interest, because both N and I are reports of general interest. Therefore, W cannot be the first report in the first segment. Questions 3 and 4 test this inference directly.

4. If W is the first report in the second segment:

PT72_Game_#1_setup_diagram 8.png

The hypothetical solutions above are not Templates, as they do not provide an exhaustive list of solutions. However, they exploit a particular restriction resulting from the application of the last rule, and yield two important inferences:

• A. Whenever I is the last report in the first segment, the game has only one possible solution. This is a critical insight that directly answers Question 5.
  
  B. Whenever I is the last report in the second segment, the game has only one possible solution.
  
  C. W cannot be the first report in the first segment.

When these inferences are added to the diagram, we arrive at the final setup for this game:

PT72_Game_#1_setup_diagram 9.png

If you find the Split Dual-Options confusing, consider forming four Templates based on the placement of N and S: two templates with N as the first report in the first segment (and S as the last report in either segment), and two templates with N as the first report in the second segment (and S as the last report in either segment):

PT72_Game_#1_setup_diagram 10.png

PT72_Game_#1_setup_diagram 11.png

PT72_Game_#1_setup_diagram 12.png

PT72_Game_#1_setup_diagram 13.png

Due to the high amount of uncertainty in this game however, these four templates only serve as partial solutions, as you cannot fill any of them in completely.

[gabs.baker]

I did the June 2014 LSAT as a practice test and completely bombed this first game, only answering numbers 3 and 5 correctly. Now during my review, I still can't seem to understand it! I read Jon's post on the blog ("The June 2014 LSAT Logic Games: What Really Happened") and I had the four templates set up correctly during the practice test but I made some inferences that completely messed it up. The problem is I can't seem to understand what the right inferences are. I inferred that W couldn't go first in either section and I couldn't go last in either section, because it states in the rules that I is longer than W. That's why I ruled out answer choice B in the first question and missed the other questions as well. If each segment goes from longest to shortest how can W be first in either one? Or since (like in the list question) I is right after N does that mean that I is the second longest therefore being longer than W?

Help through this game would be awesome!

Thanks so much,

Gabs

[Nicholas Bruno]

So let me answer the specific questions you had and please let me know if this answers your questions:

I inferred that W couldn't go first in either section and I couldn't go last in either section, because it states in the rules that I is longer than W. That's why I ruled out answer choice B in the first question and missed the other questions as well. If each segment goes from longest to shortest how can W be first in either one?

This inference would be off because W and I do not have to be in the same section. If I, for instance, was in section 1 and W in section 2, the fact that I>W really has no bearing on that scenario.

Or since (like in the list question) I is right after N does that mean that I is the second longest therefore being longer than W?

So on the last question, assuming answer choice E is correct (which it is), I and W will not be in the same segment so the I>W rule does not apply. Instead the game will look like this:

T__ __ | N W
I will be one of the last two in the first segment.

Does this make sense/answer your questions? Please follow up if not

[cnoury1221]

Hello,
I am confused about the placement of "N" and "S" as the longest and shortest reports respectively.

Rules 4 and 5 state that N is the longest of THE FIVE and S the shortest of THE FIVE. Why is N not fixed as the first report and S the last report only? I am not understanding why N can be the first in segment 1 or segment 2?

Thank you!

Carolyn

[George George]

@cnoury1221

Good Q! I can see why it is tempting to place N in 1st (in the first segment) and s in last (in the second segment). However, Rule 2 states that "Within each segment, reports are ordered by length, from longest to shortest." So there are two separate orderings happening within the overall ordering - one per segment. This allows N to be the "longest" in two different positions - at the beginning of the first segment segment, and at the beginning of the second segment. But, combined with later Rule 4 (which states that "The national report is always the longest of the five reports"), you can deduce Not Laws telling you N cannot go in the middle or end positions of either segment. Similarly, this allows s to be the shortest segment, at the end of either segment, but because of Rule 5 (which states that "The sports report is always the shortest of the five reports"), s can never go in the first or middle positions of either segment, giving you more Not Laws.

[cnoury1221]

@cnoury1221

Good Q! I can see why it is tempting to place N in 1st (in the first segment) and s in last (in the second segment). However, Rule 2 states that "Within each segment, reports are ordered by length, from longest to shortest." So there are two separate orderings happening within the overall ordering - one per segment. This allows N to be the "longest" in two different positions - at the beginning of the first segment segment, and at the beginning of the second segment. But, combined with later Rule 4 (which states that "The national report is always the longest of the five reports"), you can deduce Not Laws telling you N cannot go in the middle or end positions of either segment. Similarly, this allows s to be the shortest segment, at the end of either segment, but because of Rule 5 (which states that "The sports report is always the shortest of the five reports"), s can never go in the first or middle positions of either segment, giving you more Not Laws.

Thank you! I apologize for not seeing this sooner; I don't think I got an email notification that you replied.

[JackSparrow]

Resurrecting a thread so dead that I could start a cult of my own Apologies for that, but I was terribly confused.

With the initial constraints for N & S, you have four (2 x 2) starting options for your templates, and then you move forward from there. That makes sense. However, I don't understand why you used the limited information with the I & W constraints for additional templates. I think your explanation is in this paragraph below:

We must be careful when inferring Not Laws from this rule, because—theoretically—I could be the last report of either segment, as long as it is not in the same segment as W. Likewise, it may be possible to place W in the beginning of either segment, as long as W and I are in different segments. Such placements are likely to restrict the game considerably, which is why it is worth examining the hypothetical solutions for each:...

But it is not obvious to me that the I & W constraints must be used for templates; during the set-up, my guess was that this time was better spent working on the questions. It was only when I got to a relevant question (#5 - Global, Justify, if I'm not mistaken) and I read your explanation, that I saw the utility of having templates based on the I & W constraint.

So
(a) during set-up, how do you make the judgement call to utilize the I & W constraints to add to the templates?
(b) even if time wasn't a factor for us, I'm still not sure I see why you used I & W to make partial templates. With N & S, you have four clear starting points. But with I & W, you don't have that, so why proceed on that front even if time weren't a constraint?

Thanks for your patience. I've just barely started on my LSAT journey, so this question might be a n00b one.

[Luke Haqq]

Hi JackSparrow!

I'd be happy to try to unpack this one a bit more for you. I'll focus on addressing those last two questions you posed.

(a) during set-up, how do you make the judgement call to utilize the I & W constraints to add to the templates? (b) even if time wasn't a factor for us, I'm still not sure I see why you used I & W to make partial templates. With N & S, you have four clear starting points. But with I & W, you don't have that, so why proceed on that front even if time weren't a constraint?

In general, I understand that the judgment call can be difficult for templates! It can be a big time saver if there are only a handful of possible templates, or can potentially risk wasting time that has too many possible options. I can at least mention some aspects of this game that makes it potentially promising for the identify the templates strategy. One is that there are very few variables (5 total). Another is that it is a balanced game, fitting 5 into 5 slots (as opposed to overfunded with too many variables or underfunded with too few). Another is that there are rules imposing constraints on all of the very few variables (there are no randoms, and it's not a game that has almost no initial rules with all local questions).

All of these general facets of the game are potential evidence that there will only be a handful of templates into which the variables can fit. It's also a very important practical strategy to try to test out a game after diagramming the rules. This is especially important if you're at a point where you're deliberating whether or not to treat it as a templates game. Further, the I W variables are a good place to start in testing it out, since that gives us somewhat of a block (though as the explanation notes, it can be split up between the two segments). We already have possible locations where variables like N and S would be locked in, so working with I or W helps one see whether their placement has an effect on the other variable Whether using I or W, one could then work through putting it in each of the 5 places, and seeing what this says about the rest of the variables.

So, if we used "W" (it'd work the same for I, but would be ordered differently) starting in the first position of the first segment, we'd know where N would go:

W , __ , __ | N , __

However, this wouldn't work because of the I W rule, which is broken if I is put in the first segment. If it's in the second segment with N that won't work either, since one of those slots has to be reserved for local (S, T, W). By initially testing out W, we've already concluded it can't be in the 1st position of the 1st segment. However, we could try putting it in the second position:

__ , W , __ | __ , S/T

In this instance, there are two possible sub-templates--one where I comes in the 1st position of the 1st segment, and the other where it shares the second segment with a local program. It's worth taking note that when W is in this position, it doesn't have much of a constraining effect on variables other than I. One would have a similarly open template if W was in the 3rd slot of the 1st segment. Placing it one more over, in the 1st slot of the 2nd segment would again produce constraints regarding N:

N , I/S/T , I/S/T | W , S/T

Briefly put, the I W chunk both seems potentially constraining, and also does not have a fixed spot on the original diagram in relation to other variables. This strikes me as a good reason to work with that, choosing one of I/W and methodically moving it through various places to see how it determines other variables. However, you could arrive at the very same templates if you worked with a different variable and methodically moved it through each possible spot--you'd still be working with the I W chunk, but it wouldn't necessarily be the organizing principle for the templates.

[JackSparrow]

Luke, this is very helpful, esp on how to think through the decision of Make more templates vs Don't make more templates. Thanks for that!

[demk26]

Hi PS,

Thanks so much for this thread - it is very helpful. I'm still having trouble understanding a few of the templates, mainly because of the rule that "I is always longer than W."

If that is the case, how are Template #1 and #2 above possible? When I is in the 3rd spot in Segment 1 and W is in the first spot of Segment 2, isn't W longer than I in that case? Similarly, when W is in the 2nd spot in Segment 1 and I is in the 2nd spot of segment 2, aren't they equal in length?

Is it the fact that they are in different segments in these instances that makes those templates possible? Please let me know if I'm missing something here.

Thank you!!