Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Underfunded, Numerical Distribution game.

The scenario establishes two variable sets:

Either of these sets could be the base for this game, but a quick glance at the rules indicates that the illnesses are connected to each other by numbers, and that many of the illnesses have their symptoms specified. Thus, the illnesses are the superior choice for the base:

The rules establish both the exact numbers and the exact types of symptoms that characterize illnesses J, K, and M. The rules also establish the exact numbers—but not the exact types—of symptoms that characterize illnesses L and N. Thus, from the rules we can determine that the distribution is fixed at 2-1-2-3-1, and we also have a significant amount of information about the symptoms of each illness:

Interestingly, the third rule, which states that “illnesses J and L have at least one symptom in common,” is superfluous since it can be deduced from the other rules.

[steffanysolano]

Hi,
I need help understanding Game #2 of chapter 4 of the LSAT Game Type Training - Volume 1: LSAT Preptests 1 through 20 (Game #2- February 1992)

I am completely blank on this game and I can't seem to be able to answer a single question. I feel like I must be missing something.

Thank you,
Steffany

[Kristina Moen]

Hi Steffany,

Welcome to the Forum! When you approach a new game, the first thing to ask yourself is whether you are putting variables into [/i]order[/i] or into groups or both. Here, there is no order (no rankings, no chronology, etc.), so we are putting variables into groups. The next step is to identify the variable sets. Here, the variable sets are the five illnesses (JKLMN) and the three symptoms (FHS). One of the variable sets will be the BASE (unmoving) in your diagram, and the other variable set will be moved around the diagram. You could try both, but a quick glance at the rules tells you that the rules describe the illnesses and compare them numerically to each other (i.e. one illness has more symptoms than another or have no symptoms in common) which make the illnesses (JKLMN) a better base.

Now that you have the base of JKLMN, think about the moving variables (the symptoms FHS). We are told that each illness is characterized by at least one of the three symptoms. So each illness can have 1 - 3 symptoms. And each symptom can be repeated (i.e. two illnesses could have sneezing as a symptom). So if all the illnesses had all three symptoms, you'd see 5F, 5H, 5S. That's the maximum number variables we have to work with.

However, the rules will hem this in a bit! Let's go through this rule-by-rule.

Illness J is characterized by headache and sneezing: You add H and S to illness J - keeping in mind that this rule alone doesn't mean J cannot also have a fever. Per this rule, J could have all three symptoms. We just know J definitely has a headache and sneezing.

Illnesses J and K have no symptoms in common: A ha! Now we're moving along. If J and K have no symptoms in common, then J can't have all three! Which means J is limited to H & S. And K must have at least one symptom, so that means K has a fever. And both of those illnesses are complete. You know exactly which symptoms those illnesses have. You might indicate this with a star or some other symbol.

Illnesses J and L have at least one symptom in common: We don't know which, but L definitely has H or S (or both). So you can put H/S above L.

Illness L has a greater number of symptoms than illness K: How many symptoms does K have? Oh, K has 1. So L must have 2 or 3 symptoms. You can use ledger lines to indicate that.

Illnesses L and N have no symptoms in common: L cannot have all three symptoms then, or N would have none available! So that means L has two symptoms and N has one symptom.

Illness M has more symptoms than illness J: How many symptoms does J have? Oh, J has two. Thus, illness M has ALL the symptoms. So illness M is complete.

Here's what we ended up with:
J: H S (complete)
K: F (complete)
L: H/S __ (1 blank)
M: H S F (complete)
N: ___ (1 blank)

I hope this helps. Try answering some of the questions with this diagram.

[180bound]

Hi, I am a little confused as to what is restricting F from going into the L slot with the H and S variables. Could someone help me clear this up? The third rule states that J and L have at least one symptom in common. Could L not have F and H/S (or even F H AND S) and still satisfy this rule?

[Brook Miscoski]

180bound,

Please study the initial post and Kristina's explanation in conjunction with the game text.

Neither post indicates that F cannot be assigned to L. There is simply a blank spot, such that you do not know whether F or some other variable is assigned to L. You can visualize the blank spot as meaning h/s/f, keeping in mind that whatever you assign to L cannot be assigned to N.

L cannot have all three of the symptoms, because L and N cannot have symptoms in common, and each illness has at least one symptom. This is explained further in Kristina's post.

[oommenj2]

Hi, why can't L have 3 variables? Can't it be H SS? Why in the diagram are there only two slots?

[Adam Tyson]

L cannot have all three symptoms because then L would have to have a symptom in common with N, which is not allowed. And you cannot put the same symptom in twice and call it two symptoms - "I'm sneezing, and I am also sneezing" is still just describing a single symptom! L has to have at least one of H and S, and could have both, but whatever two things L has, N must have the third one.

[AspenHerman]

Hi! I did this problem by setting up templates to solve for solutions. I only had three answers. Is there a particular reason why the admin chose not to do them here? Am I missing something important?





For my future reference: Lesson 9 HW Numerical Distribution/Limited Solution Set Mix Game #5

[atierney]

Hi Aspen,

That's fine. You should have J, K, and M, filled out, and then the only feel variables will be the symptoms for L and N. So basically it looks like this:

F
S S
H F H
__ __ ___
J K M.

And then for L, choose two of the symptoms and give the one not chosen to N. So you can have L: HS, FS, FH, which would correspond to N: F, H, S, for a total of three possible solutions.

In terms of diagramming the game this way, you know, just as we say with all the template-type games, it really is a matter of recognition and utility, especially in the heat of the moment per se. So, I would say that I wouldn't seek out the totality of possibilities as a default, but when it works, it can definitely help narrow down the scope of the game.

[AspenHerman]

Hi Aspen,

That's fine. You should have J, K, and M, filled out, and then the only feel variables will be the symptoms for L and N. So basically it looks like this:

F
S S
H F H
__ __ ___
J K M.

And then for L, choose two of the symptoms and give the one not chosen to N. So you can have L: HS, FS, FH, which would correspond to N: F, H, S, for a total of three possible solutions.

In terms of diagramming the game this way, you know, just as we say with all the template-type games, it really is a matter of recognition and utility, especially in the heat of the moment per se. So, I would say that I wouldn't seek out the totality of possibilities as a default, but when it works, it can definitely help narrow down the scope of the game.

Okay thank you! and welcome to the forum.