Setup and Rule Diagrams

[LSAT2018]

Are there any important inferences I needed to make? I tried to look over the possibilities based on whether U was in the same spoonful as Y or Z.
General Rules
T < U ≤ X
W < Y

Possibilities (Given that Z is Random)
WT < UY < X
T < W < UYX

WT < UZ < YX
W< TY < UZX

[Adam Tyson]

Z isn't really random here, LSAT20148, because it is in the rule about U having to be paired with something. Other than that, I think you're looking pretty good here! You've identified the numerical distributions of 2-2-2 or 3-2-1 (unfixed).

I think you will find that there are many more possibilities to this game, and I wouldn't chase them all down, especially since there are only 5 questions. Don't box yourself in by thinking that these are all there are, but instead use them as a jumping off point to help you understand the game overall a little better. I didn't see any major inferences in this game, and I only chose to do a single hypothetical before heading to the questions. I based it on the 2-2-2 distribution since I saw that it really boxed U in tightly:

T would have to be in the first spoonful, U in the second, X in the third. either Y or Z would go with U. W would have to go with T since it couldn't be in the last spoonful, and then the leftover of Y and Z would go with X in the last spoonful. So it looks like this:

TW - U Y/Z - X Z/Y

Two solutions, one template, and that covers the 2-2-2. For the 3-2-1 I could see that there were too many choices for which group was what size, so I just moved to the questions figuring I'll work those out when and if I need to. That happened, for example, on question 19, where I worked out a 2-1-3 and a 2-3-1 to see what could happen when Y was alone.

[menkenj]

For this question, I started with figuring out which letters cannot go in the first or third spoonful. U,X, Y cannot go in first and W/T cannot go in third. this was my jumping off point. Did I miss any key inferences? I didn't want to spend too much time writing out scenarios and went straight to the questions after this.

[Robert Carroll]

menken,

I sketched a diagram out quickly myself on some paper and didn't really see any other inferences. Everything beyond what you said is very conditional, like "If U is not with Z, then W is before U," which is true, but why bother thinking of such a specific case? Most of the questions are local, which seems to bolster the case that minidiagrams for specific questions are going to be the way forward in this game, not an inference-heavy main diagram. The only other choice is a bunch of templates, but Adam showed earlier in this thread why templates are probably too numerous to be useful here.

Robert Carroll

[2020//Vision]

Hi there,

Could Powerscore post an explanation and breakdown for this LG and its questions? Or if you already have, could you direct me to where I can find it? I can't find it in the course or the bibles. Please and thanks!

[Jeremy Press]

Hi 2020,

Below is a basic write-up of the structure, rules, and inferences in the game, as well as a basic diagram of the same. Hopefully this helps!

1. The scenario makes clear that at least part of the task in the game is a grouping task. We must assign each of 6 letters to exactly one of 3 spoonfuls. This creates a Defined grouping scenario, in which we know that the total number of grouped variables (across the 3 spoonfuls) will equal 6.

2. The scenario does not fully define how many variables will appear in each spoonful, instead giving us a minimum (1) and maximum (3) for each spoonful. This creates a Distribution uncertainty in the game, and it is to our benefit to determine the distributional possibilities in advance. With 6 variables, and a minimum of 1 in each spoonful, there are two distributional possibilities: 2-2-2, and 3-2-1. The distribution is unfixed, because in the 3-2-1 distribution, we do not have sufficient information to determine which spoonful gets 3, which gets 2, and which gets 1 of the letters.

3. The rules clarify that there is also a sequencing component to the game, using language about which letters are "later" than other letters. These rules require us to use sequencing diagrams, and to pay attention to Not Laws.

4. The first rule places U in a later spoonful than T. This allows us to infer that T is not in the 3rd spoonful, and U is not in the 1st spoonful (see the Not Laws in the diagram).

5. The second rule is phrased negatively. Since U is not in a later spoonful than X, U is either before X, or U is in the same spoonful as X. This is represented diagrammatically using the "Double Dash" diagram. Since X will not be able to come before U in the diagram, this means we can add a Not Law for X underneath the 1st spoonful.

6. The third rules places Y in a later spoonful than W. This allows us to infer that W is not in the 3rd spoonful, and Y is not in the first spoonful. There are now only three possibilities for the 1st spoonful: T, W, and Z.

7. The fourth rule places U in the same spoonful as either Y or Z, but not both. Block diagramming represents this rule. Since it is uncertain which of Y or Z is with U, there are no additional Not Law inferences we can draw for Y or Z. The "not both" component of this rule is difficult to represent diagrammatically, so it would be advisable to highlight or underline this part of the rule so that it is not forgotten.

8. The diagram below depicts the rules, inferences, and a Template for the 2-2-2 distribution. The 3-2-1 distribution is far too open-ended to permit an efficient use of templates, so it is not advisable to pursue templates using that distribution.

September 2006 Game 4 Diagram.png

[LawSchoolDream]

Z isn't really random here, LSAT20148, because it is in the rule about U having to be paired with something. Other than that, I think you're looking pretty good here! You've identified the numerical distributions of 2-2-2 or 3-2-1 (unfixed).

I think you will find that there are many more possibilities to this game, and I wouldn't chase them all down, especially since there are only 5 questions. Don't box yourself in by thinking that these are all there are, but instead use them as a jumping off point to help you understand the game overall a little better. I didn't see any major inferences in this game, and I only chose to do a single hypothetical before heading to the questions. I based it on the 2-2-2 distribution since I saw that it really boxed U in tightly:

T would have to be in the first spoonful, U in the second, X in the third. either Y or Z would go with U. W would have to go with T since it couldn't be in the last spoonful, and then the leftover of Y and Z would go with X in the last spoonful. So it looks like this:

TW - U Y/Z - X Z/Y

Two solutions, one template, and that covers the 2-2-2. For the 3-2-1 I could see that there were too many choices for which group was what size, so I just moved to the questions figuring I'll work those out when and if I need to. That happened, for example, on question 19, where I worked out a 2-1-3 and a 2-3-1 to see what could happen when Y was alone.

Hi, why can't W be with U instead of T?

[LawSchoolDream]

Hi 2020,

Below is a basic write-up of the structure, rules, and inferences in the game, as well as a basic diagram of the same. Hopefully this helps!

1. The scenario makes clear that at least part of the task in the game is a grouping task. We must assign each of 6 letters to exactly one of 3 spoonfuls. This creates a Defined grouping scenario, in which we know that the total number of grouped variables (across the 3 spoonfuls) will equal 6.

2. The scenario does not fully define how many variables will appear in each spoonful, instead giving us a minimum (1) and maximum (3) for each spoonful. This creates a Distribution uncertainty in the game, and it is to our benefit to determine the distributional possibilities in advance. With 6 variables, and a minimum of 1 in each spoonful, there are two distributional possibilities: 2-2-2, and 3-2-1. The distribution is unfixed, because in the 3-2-1 distribution, we do not have sufficient information to determine which spoonful gets 3, which gets 2, and which gets 1 of the letters.

3. The rules clarify that there is also a sequencing component to the game, using language about which letters are "later" than other letters. These rules require us to use sequencing diagrams, and to pay attention to Not Laws.

4. The first rule places U in a later spoonful than T. This allows us to infer that T is not in the 3rd spoonful, and U is not in the 1st spoonful (see the Not Laws in the diagram).

5. The second rule is phrased negatively. Since U is not in a later spoonful than X, U is either before X, or U is in the same spoonful as X. This is represented diagrammatically using the "Double Dash" diagram. Since X will not be able to come before U in the diagram, this means we can add a Not Law for X underneath the 1st spoonful.

6. The third rules places Y in a later spoonful than W. This allows us to infer that W is not in the 3rd spoonful, and Y is not in the first spoonful. There are now only three possibilities for the 1st spoonful: T, W, and Z.

7. The fourth rule places U in the same spoonful as either Y or Z, but not both. Block diagramming represents this rule. Since it is uncertain which of Y or Z is with U, there are no additional Not Law inferences we can draw for Y or Z. The "not both" component of this rule is difficult to represent diagrammatically, so it would be advisable to highlight or underline this part of the rule so that it is not forgotten.

8. The diagram below depicts the rules, inferences, and a Template for the 2-2-2 distribution. The 3-2-1 distribution is far too open-ended to permit an efficient use of templates, so it is not advisable to pursue templates using that distribution.

September 2006 Game 4 Diagram.png

Why can't W be in spot 3? Couldn't it be WY in spot 3 if U is with Z?

[LawSchoolDream]

Hi 2020,

Below is a basic write-up of the structure, rules, and inferences in the game, as well as a basic diagram of the same. Hopefully this helps!

1. The scenario makes clear that at least part of the task in the game is a grouping task. We must assign each of 6 letters to exactly one of 3 spoonfuls. This creates a Defined grouping scenario, in which we know that the total number of grouped variables (across the 3 spoonfuls) will equal 6.

2. The scenario does not fully define how many variables will appear in each spoonful, instead giving us a minimum (1) and maximum (3) for each spoonful. This creates a Distribution uncertainty in the game, and it is to our benefit to determine the distributional possibilities in advance. With 6 variables, and a minimum of 1 in each spoonful, there are two distributional possibilities: 2-2-2, and 3-2-1. The distribution is unfixed, because in the 3-2-1 distribution, we do not have sufficient information to determine which spoonful gets 3, which gets 2, and which gets 1 of the letters.

3. The rules clarify that there is also a sequencing component to the game, using language about which letters are "later" than other letters. These rules require us to use sequencing diagrams, and to pay attention to Not Laws.

4. The first rule places U in a later spoonful than T. This allows us to infer that T is not in the 3rd spoonful, and U is not in the 1st spoonful (see the Not Laws in the diagram).

5. The second rule is phrased negatively. Since U is not in a later spoonful than X, U is either before X, or U is in the same spoonful as X. This is represented diagrammatically using the "Double Dash" diagram. Since X will not be able to come before U in the diagram, this means we can add a Not Law for X underneath the 1st spoonful.

6. The third rules places Y in a later spoonful than W. This allows us to infer that W is not in the 3rd spoonful, and Y is not in the first spoonful. There are now only three possibilities for the 1st spoonful: T, W, and Z.

7. The fourth rule places U in the same spoonful as either Y or Z, but not both. Block diagramming represents this rule. Since it is uncertain which of Y or Z is with U, there are no additional Not Law inferences we can draw for Y or Z. The "not both" component of this rule is difficult to represent diagrammatically, so it would be advisable to highlight or underline this part of the rule so that it is not forgotten.

8. The diagram below depicts the rules, inferences, and a Template for the 2-2-2 distribution. The 3-2-1 distribution is far too open-ended to permit an efficient use of templates, so it is not advisable to pursue templates using that distribution.

September 2006 Game 4 Diagram.png

I suppose I'm also slightly confused when they say spoonful do they mean 1, 2, 3 or do they mean the multiple spots within a spoon? Because initially I did draft it as 1,2,3 and come up with T-U-X as if t is in 1 u is in 2 and x is in 3, however the very first pairing question threw that structure out the window for me because they weren't really following that.

[Adam Tyson]

W CAN be with U, Dream, but not in the 2-2-2 distribution, because U must be with either Y or Z per the last rule. But in 3-2-1 distribution, you could have T in the first spoonful, WUZ in the second, and YX in the third. All the rules would be satisfied.

W cannot be in the last spoonful because it must be before Y.

There is no order within spoonfuls, just between them. Picture it in your mind - you have a spoon full of soup, and in it are some letters. It doesn't matter where in the spoon they are, just that they are together, and that some letters have to be in earlier groups than others, like W being in a spoonful before Y is.

Your T - U - X scenario is fine, and that's what happened in the scenario I just described, but that means T is in the first spoonful, U in the second, and X in the third. It has nothing to do with T being with U in the same spoonful but somehow before it.

If you're still struggling with that grouping/ordering aspect, try picturing this: There are three houses on a street, and they are numbered 1, 2, and 3. Some people live in house 1, some live in house 2, and some in house 3. T lives in a house that is lower numbered than the house that U is in. Now, it's pretty clear that T and U are not in the same house, right? And it's also clear that there is nothing about who is first in house 1, and who is second in house 1, etc. It's just about the groups of people who live in each house. That's the same as what's happening here: each spoonful is a house, and the letters are the people.