Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario and two rules combine to form the following diagram:

PT38_October_2002-G4_d1.png

This can be a challenging game due to the heavy Pattern element of the instruments. In order to effectively attack this game, you must thoroughly analyze the first rule. The rule is very carefully worded to state, “Each piece shares one instrument with the piece performed immediately before it or after it (or both)” (italics added). Thus, although a piece can share an instrument with the piece before it and with the piece after it, this is not a requirement. Therefore, there can be “breaks” within the performance order where two consecutive pieces do not share an instrument. However, these “breaks” can only appear between certain pieces, namely between the second and third pieces, and between the third and fourth pieces. Let us examine why:

Because each piece must share an instrument with another piece, we can infer that the first piece must share an instrument with the second piece, and that the fifth piece must share an instrument with the fourth piece.

The only other consecutive pieces are the second and third pieces, and the third and fourth pieces. A “break” is possible between the second and third pieces: the first and second pieces share an instrument, and then the third piece shares an instrument with the fourth, and the fourth piece shares an instrument with the fifth piece.

A “break” is also possible between the third and fourth pieces: the first and second pieces share an instrument, the second and third pieces share an instrument, and then the fourth piece shares an instrument with the fifth piece.

The restriction of the first rule, in combination with the second rule, ultimately sparks the decision to Identify the Templates. Because there are only two options for the second performance, and we know from the first rule that the first piece must share an instrument with the second piece, there seems to be an inherent limitation in the pieces that can be performed first and second. There are, in fact, only four possibilities:

When N is performed second: Because N is performed with fiddle and lute, the first piece must also be performed with fiddle or lute, and thus only T or V can be performed first.

When T is performed second: Because T is performed with fiddle and guitar, the first piece must also be performed with fiddle or guitar, and thus only N or S can be performed first.

We can now create the following four templates for the pieces:

PT38_October_2002-G4_d2.png

Within each template, there are also a limited number of possibilities for the pieces performed third, fourth, and fifth; that is, there are not six options in each template as might originally appear to be the case. Let us examine this in more detail, using the first template as an example:

Template #1 features T and N as the first two pieces. Initially, the remaining three pieces—O, S, and V—appear to have six possible orders: O-S-V; O-V-S; S-O-V; S-V-O; V-O-S; and V-S-O. However, due to the restriction of the first rule, only three of these possibilities are valid:

T-N-O-S-V: this possibility fails because V does not share an instrument with S
T-N-O-V-S: this possibility fails because S does not share an instrument with V
T-N-S-O-V: this possibility is a valid solution with no “break”
T-N-S-V-O: this possibility fails because S does not share an instrument with either N or V
T-N-V-O-S: this possibility is a valid solution with no “break”
T-N-V-S-O: this possibility is a valid solution with a “break” between the third and fourth piece

This same type of analysis can be applied to each of the other templates, and each of the other templates also contains three possible solutions:

Template #2. The three solutions are:

V-N-T-O-S
V-N-T-S-O
V-N-O-S-T

Template #3. The three solutions are:

N-T-S-O-V
N-T-S-V-O
N-T-V-O-S

Template #4. The three solutions are:

S-T-N-O-V
S-T-N-V-O
S-T-O-V-N

An examination of the solutions for each template reveals an interesting pattern: the remaining three pieces in each template contain one piece that shares an instrument with each of the other two pieces, but those two other pieces do not share an instrument with each other. For example, in Template #2, S shares an instrument with both O and T, but O and T do not share an instrument with each other. In Template #3 (and Template #1), O shares an instrument with both S and V, but S and V do not share an instrument with each other. In Template #4, V shares an instrument with both N and O, but N and O do not share an instrument with each other. This pattern in part limits the total number of solutions since the two pieces that do not share an instrument cannot be performed fourth and fifth.

In total, the game contains twelve solutions, but it would be quite time-consuming to list each possibility at the start of the game. We recommend that you instead proceed with the four templates, and make note of the basic relationships among the remaining three variables in each template. The templates prove critical to answering several of the questions.

[rallawatt]

Need some help on this game, just not really sure at all how to properly attack it efficiently.

LSAT Content Removed by Admin – October 2002, Game 4, Questions 20-24 (musicians)

Being that there aren't a lot of rules, I decided that my best approach would be to create different templates, one with Nexus 2 and the other with Tailwind 2.

Someone want to explain how they would create their initial setup?

[rallawatt]

Specifically questions 20, 22, 24.

[Nikki Siclunov]

You are correct - the best way to solve this game is with templates.

We have 5 pieces to arrange in order: NOSTV

Each piece is performed with 2 instruments, as follows:

N = fl
O = hm
S = gh
T = fg
V = lm

Each piece shares one instrument with the piece performed immediately before it or after it (or both). This is the most important rule in the game, and it's crucial to internalize it before proceeding to formulate a set-up.

Because either N or T must be second, the first piece must share an instrument in common with either N or T. This produces 4 templates:

T N (O, S, V)
V N (O, S, T)
N T (O, S, V)
S T (N, O, V)

Although I wouldn't identify each possibility with respect to the last 3 pieces, keep in mind that the most powerful variable in each template will be the last piece performed, because it needs to share an instrument with the 4th piece.

Hope this helps!

[alee]

Hi,

What would you advise to be the best way to tackle game 4 in section II of preptest 38 (Nexus, Onyx, Synchrony...)?

I generally have a bit of trouble with games that don't have many rules, and require primarily patterns inferences, (like this one), because I find them really hard to diagram (too many hypotheticals, in general).

Your help would be appreciated as always,

Thanks!

[Dave Killoran]

Hey Alex,

I've always thought this is a tough game because it is so odd. To help explain this, let me pull part of the the setup explanation from our LSAT Logic Games Encyclopedia, Volume 2 (http://shopping.powerscore.com/product_ ... 873ED91129).

In order to effectively attack this game, you must thoroughly analyze the first rule. The rule is very carefully worded to state, “Each piece shares one instrument with the piece performed immediately before it or after it (or both)” (italics added). Thus, although a piece can share an instrument with the piece before it and with the piece after it, this is not a requirement. Therefore, there can be “breaks” within the performance order where two consecutive pieces do not share an instrument. However, these “breaks” can only appear between certain pieces, namely between the second and third pieces, and between the third and fourth pieces. Let us examine why:

• Because each piece must share an instrument with another piece, we can infer that the first piece must share an instrument with the second piece, and that the fifth piece must share an instrument with the fourth piece.
  
  The only other consecutive pieces are the second and third pieces, and the third and fourth pieces. A “break” is possible between the second and third pieces: the first and second pieces share an instrument, and then the third piece shares an instrument with the fourth, and the fourth piece shares an instrument with the fifth piece.
  
  A “break” is also possible between the third and fourth pieces: the first and second pieces share an instrument, the second and third pieces share an instrument, and then the fourth piece shares an instrument with the fifth piece.

The restriction of the first rule, in combination with the second rule, ultimately sparks the decision to Identify the Templates. Because there are only two options for the second performance, and we know from the first rule that the first piece must share an instrument with the second piece, there seems to be an inherent limitation in the pieces that can be performed first and second. There are, in fact, only four possibilities:

• When N is performed second: Because N is performed with fiddle and lute, the first piece must also be performed with fiddle or lute, and thus only T or V can be performed first.

When T is performed second: Because T is performed with fiddle and guitar, the first piece must also be performed with fiddle or guitar, and thus only N or S can be performed first.

With this information, we can now create the following four templates for the pieces:


Template #4: S T ( N, O, V )
Template #3: N T ( O, S, V )
Template #2: V N ( O, S, T )
Template #1: T N ( O, S, V )
..1..2..3..4..5


That's a start, so please let me know if that helps. Thanks!

[alee]

Hi Dave,

Thanks for that, the templates are helpful although I did have 2 further queries.
Regarding 22, I ended up writing out 4 hypotheticals and (corresponding to the 4 templates) since the restriction that each piece shares an instrument with the piece immediately following means that there are only 4 possibilities in total. However, doing this was pretty time consuming, are there any other ways to eliminate the incorrect answer choices?

Regarding 24, whilst E is immediately eliminated by the rules and A is eliminated by the templates you mentioned, B C and E were quite time consuming to choose from. I solved it by writing out 3 templates with O3 (option B), which also happened to eliminate the possibility of V4 (option C).

The time consuming aspect of this game is the number of instruments and remembering which piece has which instrument in common with which...

Thanks for your help with the templates, but do you have any time-saving tips with 22 and 24?

[Dave Killoran]

Hi Alex,

In both those questions you've run into instances where the test makers wanted to consume your time, so there are no real back doors or shortcuts to solve those questions.

In #22, it's a straight hypothetical solution.

In #24, this is a classic final game question—time-consuming and frustrating. If S is performed fifth, then either O or T must apparently be performed fourth. But, T cannot be performed fourth because there is no workable hypothetical with T fourth and S fifth (N must then be performed second, V must be performed first, and then O is left to be performed third, creating a V-N-O-T-S hypothetical that violates the first rule). Hence, O must be performed fourth, and this inference eliminates answer choices (B) and (C). Now that we have established that O will be performed fourth and S will be performed fifth, we can examine the templates to see if any possibilities have been eliminated. Because Template #4 features S as the first performance, we can eliminate Template #4 from consideration. The remaining three templates each feature N as either the first or second performance, and thus we can eliminate answer choice (A). The only remaining answer choices are (D) and (E)—V performed either first or second. Of our three templates (#1, #2, and #3), only Template #2 features V as either the first or second performance, and thus Template #2—which features V as the first performance—proves answer choice (D) correct.

The truth is that on occasion the test makers design questions in a way that they know will consume time because there is no easy way to see the right solution. Hopefully you have the rest of the game set up well because when this occurs, there are always other questions that can be solved quickly (like #20 and #23).

Please let me know if that helps, even if only a little

Thanks!

[SherryZ]

Hi Nikki,

I also used the way you mentioned but I still solved this question sooo slowly I feel so frustrated and worried that I cannot finish LG in 35 min


---Sherry

[Nikki Siclunov]

Hi Sherry,

What drives your speed in Logic Games is, generally speaking, the ability to make powerful inferences from combining two or more rules. Occasionally, speed is also a product of recognizing that the game is sufficiently restricted to set up with templates (which was the case in the game mentioned above). Keep in mind, however, that each approach requires an initial investment of time, which you hope to recoup later on. As in real life, if your investment is too small, then you are unlikely to get a large return on it; inversely, if you invest too much time reaching for these hard-to-get inferences, or decide to make templates when you shouldn't, then the cost of that investment might outweigh the benefits. The ideal approach to logic games, then, is a balancing act: naturally, it takes awhile to perfect it.

My advice to you would be this: make a list of all the games you've done that are taking you more than 10 mins to solve. Think of it as your Re-Do list for later. After you acquire enough experience with the test, re-do each one of these games. Students often assume, erroneously, that each game can only be done once. In fact, improvement often results from repeatedly engaging in the type of cognitive task that you initially found to be difficult.

Hope this helps!