Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

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

This game is primarily a Sequencing game, but the last rule moves it into a Linear classification (which is not that significant of a change—all Sequencing games are Linear; Sequencing games just have Sequencing rules only).

The first two rules can be diagrammed as follows:

First rule:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_1.png

Second rule:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_2.png

Combined, they appear as follows:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_3.png

These two rules jointly establish that M, L, and P cannot be last, and that H and J cannot be first. The combination of the two rules is also unique, because 5 of the 6 variables are addressed; only G is not included.

The third rule is more complex, and, as has been occurring more frequently in recent years, produces two mutually exclusive scenarios. Conditionally, the rule can initially be diagrammed as:

• M P H G

Because there are not ties in this game (and thus order is a two-value system), the contrapositive appears as:

• G H P M

The operating result of this rule is that the game takes two different directions, each of which requires its own template. More on this approach shortly.

The fourth and final rule establishes a G Not Law on the sixth position:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_4.png

Note that, because the first two rules establish that M, L, and P cannot be last, and because the fourth rule establishes that G cannot be last, only two actors could be last: H or J.

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_5.png

With the basic rules in place, let us examine the templates created by the third rule.

Template #1

This template occurs under the M P H G aspect of the third rule. With H appearing earlier than G, only J can be last under this template. With J appearing last, the second rule is automatically satisfied and can be disregarded at this point. M and L must still appear earlier than H (from the first rule), and P is required to appear later than M (from the third rule). Thus, the full diagram appears as:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_6.png

Template #2

This template occurs under the G H P M aspect of the third rule, and is the more challenging of the two templates to diagram. Starting from the base diagram of the first and second rules combined, to account for G H, we can add a line from H up to G; similarly, we can do the same between P and M, although this is not the most elegant of solutions from a visual standpoint:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_7.png

With the two conditions added, only G, L or P can appear first, and only H or J can appear last:

powerscore_M12_T3_J2010_LG_explanations_game_2_diagram_8.png

[clarocca]

Regarding Rule #3

The rule is diagrammed as M>P ---> H>G

Why is the contrapositive G>H-----P>M
and not
H>G --> M>P (with each variable crossed out) ?

[Dave Killoran]

Hi Clarocca,

Thanks for the question! What we've done is converted the contrapositive terms into their actual operating meaning. So, let's look at the rule and explain how that works. The initial rule diagram is:


M > P H > G


So, the contrapositive is then:


H > G M > P


That's good, but what does H > G really mean? If H can't be earlier than G, and there are no possible ties in the game. what that statement really means is that G > H. Thus, because that's so much easier to understand, we simply converted that diagram directly into that meaning, and did the same with M > P, resulting in this diagram:


G > H P > M


Please let me know if that helps. Thanks!

[clarocca]

WOW! Yes, that helped so much. I can't believe I didn't come to that conclusion on my own. Thank you so much. It was driving me crazy.

[nutcracker]

Hi Dave,

I have a question about using the "Identify the Templates" method for this game. I understand that M>P H>G
and G>H P>M are mutually exclusive possibilities, but I don't think they are exhaustive. For example, it is theoretically possible to have H>G and P>M at the same time.

I get the impression that "Identify the Templates" is most effective when we can list all the possible templates, not just some possible templates. However, I also remember that there are times when rules in the "if A > B then C > D" format lead to templates that perfectly encompass all the possibilities. Does it depend on the nature of the rules? If so, could you please go over what exactly makes a rule more amenable to the template method? Thanks a lot!

[Adam Tyson]

You are correct, nutcracker, and when I do this game with my class I always show them the third template that you noticed. In fact, any time I see a conditional rule in a logic game, I suggest considering three options:

1. The sufficient and necessary conditions both occur
2. Neither condition occurs
3. The necessary condition occurs and the sufficient condition does not

The guidelines for when it is a good idea to pursue templates and when it is not are fairly loose, and there is no simple, clean answer to that question. What makes a game a good template game is somewhat ephemeral. At a high level, it's about whether you recognize that the rules severely limit the number of approaches to take to the game. Not necessarily the number of solutions - I was just doing a template game with someone that had 16 possible solutions, but only 4 templates. Instead, look for multiple, interlocking restrictions that force variables into only a few possible relationships. That could be a long sequence in a linear game, a large block coupled with some numeric distributions in a grouping game, an influential variable or two that forces several variables either into or out of a solution, and more.

With Pure Sequencing games, a strong indication that templates are called for is the presence of a conditional rule or a rule that says "this or that, but not both". When I see "but not both" then I know I am looking at two templates, at least. Two rules like that in a pure sequencing game and I am bracing myself for four templates to account for all the combinations those will create.

If you are going to pursue templates, pursue them all. If you start down that path and get good results, keep going! If you find yourself saying "well that wasn't very helpful", consider abandoning that approach and trying something else or just moving on to the questions. I tend to attempt templates on about 3/4 of the games, way more often than they are called for. I find quickly whether they are working or not, and end up following through on them only about half the time. The rest of the time, I take note of what I learned from the experience, maybe make an inference or two, and I count myself fortunate for having gotten what I did and not wasting too much time on it.

I wish we had clearer rules for when to tell you to do templates! It's much more holistic than it is formulaic. It's one of those "you'll know it when you see it" things that comes with practice, practice, practice. Keep hammering away at it, trying templates frequently until you start to get a good sense of when you should and when you should not go down that path.

Good luck!

[nutcracker]

Thanks Adam for such a lengthy reply! I'll try to practice more while keeping in mind all this information

[SwanQueen]

You are correct, nutcracker, and when I do this game with my class I always show them the third template that you noticed. In fact, any time I see a conditional rule in a logic game, I suggest considering three options:

1. The sufficient and necessary conditional both occur
2. Neither condition occurs
3. The necessary condition occurs and the sufficient condition does not

The guidelines for when it is a good idea to pursue templates and when it is not are fairly loose, and there is no simple, clean answer to that question. What makes a game a good template game is somewhat ephemeral. At a high level, it's about whether you recognize that the rules severely limit the number of approaches to take to the game. Not necessarily the number of solutions - I was just doing a template game with someone that had 16 possible solutions, but only 4 templates. Instead, look for multiple, interlocking restrictions that force variables into only a few possible relationships. That could be a long sequence in a linear game, a large block coupled with some numeric distributions in a grouping game, an influential variable or two that forces several variables either into or out of a solution, and more.

With Pure Sequencing games, a strong indication that templates are called for is the presence of a conditional rule or a rule that says "this or that, but not both". When I see "but not both" then I know I am looking at two templates, at least. Two rules like that in a pure sequencing game and I am bracing myself for four templates to account for all the combinations those will create.

If you are going to pursue templates, pursue them all. If you start down that path and get good results, keep going! If you find yourself saying "well that wasn't very helpful", consider abandoning that approach and trying something else or just moving on to the questions. I tend to attempt templates on about 3/4 of the games, way more often than they are called for. I find quickly whether they are working or not, and end up following through on them only about half the time. The rest of the time, I take note of what I learned from the experience, maybe make an inference or two, and I count myself fortunate for having gotten what I did and not wasting too much time on it.

I wish we had clearer rules for when to tell you to do templates! It's much more holistic than it is formulaic. It's one of those "you'll know it when you see it" things that comes with practice, practice, practice. Keep hammering away at it, trying templates frequently until you start to get a good sense of when you should and when you should not go down that path.

Good luck!

Hey Adam!

Firstly, thank you to Nutcracker for this great question, and for you for this elaborate answer!

I was wondering, what is the "but not both" quality in this specific question?

Thanks in advance!

[Robert Carroll]

Swan,

This not a situation where there is a "but not both" quality to the game. Instead, there is a conditional rule in this Pure Sequencing game. Note what Adam said about the triggers for templates in such games:

With Pure Sequencing games, a strong indication that templates are called for is the presence of a conditional rule or a rule that says "this or that, but not both".

So a conditional rule or a rule that has a "but not both" quality would each indicate that templates are likely to be a good idea. This game has a conditional rule, fitting the first of those criteria.

Robert Carroll

[atdale1980]

Let me know if this should be its own thread. I got all of the questions right and made the same templates, albeit they looked a little differently. My problem is time. I've already taken the LSAT once and LG has been my most accurate consistently on PTs, whether it's a full one, timed or untimed. Games like these though, with List questions, trip me up the most, whether it's Global or Local. Is there a most effecient way of setting these up to get to diagram the base and templates, making inferences? Especially when one of the rules is like #3 showing 2 paths.

My diagram and templates looked like the attached.