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- Wed Mar 09, 2011 4:55 pm
#94149
Setup and Rule Diagram Explanation
This is a Pattern game.
This game from December 1994 was repeated as the third game of the February 1997 LSAT. The repeat version featured a train making five trips around a circle containing stops P, Q, R, S, and T. On each trip the train stopped at exactly three of the five stops. No stop could be repeated three trips in a row, and each stop had to be visited at least once in any two-trip period.
Let’s first examine the participation of the clans and the overall cycle. Each cycle ends when each of the five clans has participated exactly three times each, so there are a total of fifteen participations during the life of the cycle. Because there are only three participations each year, a cycle must last for exactly five years (this is the correct answer to question #20). This can be diagrammed as:
Determining the length of the cycle effectively makes the third rule “dead” (meaning it has been appropriately captured and no longer needs to be considered actively in each question). The fourth rule is captured by understanding that each clan must be used three times within each cycle:
Those fifteen clan participations make up each cycle, and once identified are easy to understand and represent.
Now that the basic setup is established, we move to the most difficult part of the game. With the third and fourth rules under control, only the first and second rules require constant monitoring in this game. But, as in most Pattern games, these two rules do not address any specific variables, but instead address the global behavior of all variables. As is often the case in Pattern games, there is a broad-based pattern that controls the variables in a predictable way. Let’s look at the two rules more closely and see if we can deduce the pattern.
The first rule establishes that each clan participates at least once in any two consecutive years (italics added for emphasis). The “any two consecutive years” is the most critical part. That means each clan has to participate at least once in years 1-2, at least once in years 2-3, at least once in years 3-4, and at least once in years 4-5. That is an extremely restrictive rule and it dramatically affects how the clans are used. For example, let’s assume that clans N, O, and P participate in the first year:
With the first year filled, for Q and R to comply with the first rule they must participate in the second year:
The third clan in the second year would then be one of N, O, or P. Let’s say that N was the clan participating in the second year. If that’s the case, then from the action of the second rule, N could not participate in the third year:
Let’s take a moment to review how N stands in respect to the first rule :
N participates twice in years 1-2.
N participates once in years 2-3.
Currently, N does not participate in years 3-4. Thus, because N cannot participate in the third year, N must participate in the fourth year:
With N participating in the fourth year, N participates once in years 3-4 and years 4-5.
Thus, N participates a total of three times, and conforms to both the first and second rules.
Note that N now participates in years 1-2-4. O and P, the other two clans that participated in the first year, would have to participate in the third year (establishing both with a 1-3 start to the cycle). This reveals an interesting fact: for the three clans who participate in the first year, one of the three participates in the second year (1-2) and the other two participate in the third year (1-3). This is the start of the pattern, and as you might expect, if the cycle starts with a pattern, it ends with one too.
We could continue to show how the variables work to construct the entire pattern, but we recommend that you play with some of the options and watch how the patterns form. What you will ultimately find is that the rules produce a pattern where each cycle contains five distinct participation sequences. Each clan must fit one of the five sequences, and each cycle must contain all five of the sequences. The five sequences are:
In our example, N fit the 1-2-4 sequence, and one of O and P would fit the 1-3-4 sequence and the other would fit the 1-3-5 sequence.
But, what if you can’t determine the pattern during the setup? Admittedly, the patterns above are difficult to deduce during the game. Pattern game setups typically contain minimal information, and if you do not see the patterns for this game (or any Pattern game) during the setup, move to the following two types of questions first:
1. List questions
List questions allow you to work with pre-made solutions and to simply use the rules to eliminate answer choices. Deriving the correct answer gives you a hypothetical that adds to your overall game knowledge. In this game questions #18 and #24 are List questions.
2. Questions with the greatest amount of local information
These questions give you the best chance to work directly with the variables while still solving questions, and hopefully working with the questions will give you a better sense of what is occurring in the game on a global level. In this game, then, to apply that approach you would begin with questions #22, #23, or #24 and use the hypotheticals produced by those questions to gain an understanding of how the rules interact.
This is a Pattern game.
This game from December 1994 was repeated as the third game of the February 1997 LSAT. The repeat version featured a train making five trips around a circle containing stops P, Q, R, S, and T. On each trip the train stopped at exactly three of the five stops. No stop could be repeated three trips in a row, and each stop had to be visited at least once in any two-trip period.
Let’s first examine the participation of the clans and the overall cycle. Each cycle ends when each of the five clans has participated exactly three times each, so there are a total of fifteen participations during the life of the cycle. Because there are only three participations each year, a cycle must last for exactly five years (this is the correct answer to question #20). This can be diagrammed as:
Determining the length of the cycle effectively makes the third rule “dead” (meaning it has been appropriately captured and no longer needs to be considered actively in each question). The fourth rule is captured by understanding that each clan must be used three times within each cycle:
Those fifteen clan participations make up each cycle, and once identified are easy to understand and represent.
Now that the basic setup is established, we move to the most difficult part of the game. With the third and fourth rules under control, only the first and second rules require constant monitoring in this game. But, as in most Pattern games, these two rules do not address any specific variables, but instead address the global behavior of all variables. As is often the case in Pattern games, there is a broad-based pattern that controls the variables in a predictable way. Let’s look at the two rules more closely and see if we can deduce the pattern.
The first rule establishes that each clan participates at least once in any two consecutive years (italics added for emphasis). The “any two consecutive years” is the most critical part. That means each clan has to participate at least once in years 1-2, at least once in years 2-3, at least once in years 3-4, and at least once in years 4-5. That is an extremely restrictive rule and it dramatically affects how the clans are used. For example, let’s assume that clans N, O, and P participate in the first year:
With the first year filled, for Q and R to comply with the first rule they must participate in the second year:
The third clan in the second year would then be one of N, O, or P. Let’s say that N was the clan participating in the second year. If that’s the case, then from the action of the second rule, N could not participate in the third year:
Let’s take a moment to review how N stands in respect to the first rule :
N participates twice in years 1-2.
N participates once in years 2-3.
Currently, N does not participate in years 3-4. Thus, because N cannot participate in the third year, N must participate in the fourth year:
With N participating in the fourth year, N participates once in years 3-4 and years 4-5.
Thus, N participates a total of three times, and conforms to both the first and second rules.
Note that N now participates in years 1-2-4. O and P, the other two clans that participated in the first year, would have to participate in the third year (establishing both with a 1-3 start to the cycle). This reveals an interesting fact: for the three clans who participate in the first year, one of the three participates in the second year (1-2) and the other two participate in the third year (1-3). This is the start of the pattern, and as you might expect, if the cycle starts with a pattern, it ends with one too.
We could continue to show how the variables work to construct the entire pattern, but we recommend that you play with some of the options and watch how the patterns form. What you will ultimately find is that the rules produce a pattern where each cycle contains five distinct participation sequences. Each clan must fit one of the five sequences, and each cycle must contain all five of the sequences. The five sequences are:
In our example, N fit the 1-2-4 sequence, and one of O and P would fit the 1-3-4 sequence and the other would fit the 1-3-5 sequence.
But, what if you can’t determine the pattern during the setup? Admittedly, the patterns above are difficult to deduce during the game. Pattern game setups typically contain minimal information, and if you do not see the patterns for this game (or any Pattern game) during the setup, move to the following two types of questions first:
1. List questions
List questions allow you to work with pre-made solutions and to simply use the rules to eliminate answer choices. Deriving the correct answer gives you a hypothetical that adds to your overall game knowledge. In this game questions #18 and #24 are List questions.
2. Questions with the greatest amount of local information
These questions give you the best chance to work directly with the variables while still solving questions, and hopefully working with the questions will give you a better sense of what is occurring in the game on a global level. In this game, then, to apply that approach you would begin with questions #22, #23, or #24 and use the hypotheticals produced by those questions to gain an understanding of how the rules interact.
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Dave Killoran
PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
