Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Defined-Fixed, Balanced Grouping game.

This is a very tricky game, and most students set the game up by focusing on the three cities. However, the last rule leads to the key inference of this game. Take a moment to re-examine that rule. Most students do not completely grasp the meaning behind this rule, but any rule that addresses the numbers in a game will be important and must be completely understood. If each student visits one of the cities with another student, then the minimum group size is two. With only five students, we can deduce that there are only two groups of students in this game: one group of two students, and another group of three students. These two groups control the game, and they also show that only two of the three of the cities can be visited.

With the two groups established, we can analyze the grouping rules in the game and make inferences.

Because S and P must visit different cities, they must be in different groups. Thus, although we do not know which group S or P is in, they occupy a space in each group. This fact affects the H and R block (who says the makers of the LSAT don’t have a sense of humor?), because there is not enough room in the group of two for the HR block. Thus, H and R must be in the group of three, and L must be in the group of two:

D92_Game_#1_setup_diagram 1.png

Adding in a few of the other rules and showing the three cities leads to the final diagram:

D92_Game_#1_setup_diagram 2.png

[LSAT2018]

What makes this a Defined-Fixed, Balanced Grouping game, rather than a Defined-Moving game? It involves numerical distributions and you're not sure which cities have 2 or 3 students.

[Jon Denning]

Good question! I'll answer in two parts, one about numerical distributions in general, the other about the fixed/unfixed idea.

The reason numerical distribution games are classified as such is based on uncertain or changing numbers, which this game doesn't have! That is, we know precisely the size of the groups, and only have to worry about the final composition of each and where the triple and double groups will be placed. If, instead, we sometimes had a 3-2-0 distribution and at other times had a 2-2-1 distribution, then that numerical uncertainty would play a far greater role and we'd make it a central focus (and label it accordingly).

Secondly, the reason we call this fixed and not unfixed (or moving) is that there are restrictions on where the double group can go: L is always in the double, and L must go to either M or T. So, since it can't be placed everywhere, the distribution isn't entirely random and thus we list it as fixed (Note: fixed doesn't have to mean "only one option;" it just means not completely open)

[tgracee]

Why is the game only a group of 2 and 3, rather than a students being able to repeat to fill all three cities?

[Dave Killoran]

Because of the first line of the scenario, which states that: "Each of five students...will visit exactly one of three cities..." (italics added). So, they can't repeat. Always look for rules/limitations like this, because if they aren't there the number of possibilities usually rises dramatically.

Please let me know if that helps. Thanks!

[Robert Carroll]

grace,

This paragraph of Dave's explains why that's true:

This is a very tricky game, and most students set the game up by focusing on the three cities. However, the last rule leads to the key inference of this game. Take a moment to re-examine that rule. Most students do not completely grasp the meaning behind this rule, but any rule that addresses the numbers in a game will be important and must be completely understood. If each student visits one of the cities with another student, then the minimum group size is two. With only five students, we can deduce that there are only two groups of students in this game: one group of two students, and another group of three students. These two groups control the game, and they also show that only two of the three of the cities can be visited.

Students cannot repeat: the scenario says that each student visits exactly one city. That combined with the last rule leads to the inference that one city is unused, one city has 2 people, and one has 3.

Robert Carroll

[kupwarriors9]

Hi!

This is more of a conditional reasoning question. Hypothetically, if Paul visits Toronto or Montreal with Lori as a group of two, can H, R & S still visit Vancouver? Or is H 'banned' from visiting Vancouver when Paul isn't in Vancouver. I find I get these diagrams mixed up.

So, to illustrate:
Hv --> Pv {BUT} can H still go to Vancouver without P?

Thanks,
KW9

[atierney]

Hi,

The rule "If Paul visits Vancouver, Hubert visits Vancouver with him," is interpreted as meaning Paul can't visit Vancouver unless Hubert also visits Vancouver. Notice that it would be a Mistaken Reversal to state that Hubert can't visit Vancouver unless Paul visits Vancouver. If P visits V -> H visits V, but NOT if H visits V -> P visits V. So, in answer to your question, there's nothing preventing Paul and Lori from making a secret rendezvous in Montreal, while H and R (who do have to go to the same city) meets up with Sharon in Vancouver.

[kupwarriors9]

Thank you!!!!!!!!!

Hi,

The rule "If Paul visits Vancouver, Hubert visits Vancouver with him," is interpreted as meaning Paul can't visit Vancouver unless Hubert also visits Vancouver. Notice that it would be a Mistaken Reversal to state that Hubert can't visit Vancouver unless Paul visits Vancouver. If P visits V -> H visits V, but NOT if H visits V -> P visits V. So, in answer to your question, there's nothing preventing Paul and Lori from making a secret rendezvous in Montreal, while H and R (who do have to go to the same city) meets up with Sharon in Vancouver.

[parisielvirac]

Hi, with the last rule and "exactly one city" stated in the scenario, how is the possibility that all five of them going to one city excluded? since it says "Each student visits one of the cities with ATLEAST another..." leaving the possibility of all five of them together open?

I dont understand the effect "exactly one city" has on the scenarios. Can someone explain please? Thanks