Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Unbalanced: Underfunded, Identify the Templates game.

The game scenario indicates that five clerks must stock nine numbered aisles, creating an Underfunded Linear game:

PT34-June2001_LGE-G1_srd1.png

The information in the scenario and the first rule establishes that five clerks are in a fixed 2-2-2-2-1 Numerical Distribution of aisles stocked-to-clerks:

PT34-June2001_LGE-G1_srd2.png

The second and third rules establish that K stocks aisle 2 and that M does not stock aisle 1:

PT34-June2001_LGE-G1_srd3.png

The fourth rule creates a not-block for J:

PT34-June2001_LGE-G1_srd4.png

The fifth rule creates the following block:

PT34-June2001_LGE-G1_srd5.png

While the initial thought may be to place this block in aisles 1-2-3, from the third rule M cannot stock aisle 1, and so this block must appear elsewhere in the setup. Thus, there are some limitations on which aisles K can stock, namely that K cannot stock aisles 1, 3, and 9:

PT34-June2001_LGE-G1_srd6.png

Note that while M cannot stock aisle 1, M could conceivably stock aisle 3 if K stocked aisle 4 and M stocked aisle 5.

The sixth rule establishes that exactly one of L’s aisles is an end aisle:

PT34-June2001_LGE-G1_srd7.png

The seventh rule creates a sequence where O’s aisle is numbered higher than both of K’s aisles, but numbered lower than at least one of L’s aisles. This rule can be combined with the block created in the fifth rule:

PT34-June2001_LGE-G1_srd8.png

This rule has a dramatic effect on the game because it involves so many variables, and because the MKM block is limited in where it can be placed. Because M cannot stock aisle 1, the block can be placed no lower than aisles 3-4-5. And, because O and L must stock aisles behind M, the MKM block cannot be placed on aisle 8 or 9. Thus, the MKM block is either in aisles 3-4-5, 4-5-6, or 5-6-7. Consequently, O must stock aisle 6, 7, or 8. Because of the limited placement of the block, only three templates exist:

PT34-June2001_LGE-G1_srd9.png

In examining the above templates, certain limitations become apparent:

• Aisle 1 must be stocked by J or L. This occurs because M, K, and O cannot stock aisle 1.

• Aisle 5 must be stocked by K or M. This occurs because MKM block must be placed on aisle 5.

• Aisle 9 must be stocked by J or L. This occurs because M, K, and O cannot stock aisle 9.

• Template #3, with the MKM in 5-6-7, is the most restricted, with only two solutions.

With the three templates in hand, the game becomes considerably easier.

[lizk89]

I'm concerned with the following rule:

"Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's."
__________________________

Does "Olga's aisle is numbered higher than EITHER of Kurt's aisles..." mean at least one of them or both of them?

I was operating under the impression that it meant: O at least once before K but my study partner just finished the game with a perfect score and tells me that it means: O before K both times that K appears.

Help!

[Adam Tyson]

Hey Liz. A rule worded like that does mean higher than both. But be careful - when a linear game gives a rule about "A is numbered higher than B", that usually means AFTER rather than before (because your setup will usually have the linear base running from 1 at the left to higher numbers as you move to the right). I'm not looking at that particular game right now, but if you set up your base as 1..2..3..4..5, etc., and O is numbered higher than K, then it means that K is BEFORE O and not the other way around.

Hope that helps!

Adam

[Dave Killoran]

Hey Liz,

Let me add a note to Adam's explanation.

In this situation, I think it was the "either" that caused you problems, because you saw that and translated it into the "at least one" definition. But, that definition only applies to the classic "either/or" phrasing (and even that can change if "than" is added). In this instance, although they used "either," they didn't use "or," and that's one indication that things are different. Let's look at it more closely:

"Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's."

I put italics on the key phrase here. The operating result is, as you suspect, that the "than either" usage means "both," and not just "at least one." From an English standpoint, in most cases, “either…or” means “one or the other.” For example, if we see the rule “either A or B must attend,” this means that at least one of the two must be there; they are not both required to attend. In this particular case, however, we should note that the word “either” is preceded by the conjunction “than” and is used at the end of a comparison. Where this is the case, “either” actually means “both.” For example, “He is taller than either of the other two boys on the team” means that he is the tallest of the three, and “I like History better than either Biology or Physics” means that History is my favorite of the three classes mentioned. In the same sense, if I graduated more recently than either of my brothers, I must be the most recent graduate.

They've done something similar before as well: Go check out the October 2004 Logic Games section, #13-17, in the fifth rule:

"The site visited third dates from a more recent century than does either the site visited first or that visited fourth."

In that case, they also meant "both." Could they have been clearer in both instances? No doubt they could have. But, I’ve discovered over time that there are fair number of situations where I wish they had stated it more clearly (for example, saying “both” in this case would have made it easier). I think that sometimes they aren’t interested in perfect clarity, but rather in whatever they feel is minimally defensible in case someone asks about it.

Please let me know if that helps. Thanks!

Note: parts of this post borrowed from my previous discussion about the October 2004 rule, at http://forum.powerscore.com/lsat/viewto ... 3487#p3466

[lizk89]

Appreciate both your comments very much!

[anellis]

can you direct me on how to find details on this game including the proper set up?
Game #1 about clerks in a supermarket

[Dave Killoran]

Hi Anellis,

This game sets up as a standard Basic Linear game, except that with only five clerks we have an underfunded game with a fixed 2-2-2-2-1 Numerical Distribution of aisles stocked-to-clerks:

2 2 2 2 1
J K L M .....O

The rules slowly unwind until you reach the seventh rule. This rule has a dramatic effect on the game because it involves so many variables, and because the MKM block from the fifth rule is limited in where it can be placed. Because M cannot stock aisle 1, the block can be placed no lower than aisles 3-4-5. And, because O and L must stock aisles behind M, the MKM block cannot be placed on aisle 8 or 9. Thus, the MKM block is either in aisles 3-4-5, 4-5-6, or 5-6-7. Consequently, from the last rule, O must stock aisle 6, 7, or 8. Because of the limited placement of the block, only three templates exist based on the MKM block positions, and the best way to attack this game is to diagram out the three solutions.

When you create the templates, certain limitations become apparent:

• Aisle 1 must be stocked by J or L. This occurs because M, K, and O cannot stock aisle 1.
• Aisle 5 must be stocked by K or M. This occurs because one of the variables in the MKM block must be placed on aisle 5.
• Aisle 9 must be stocked by J or L. This occurs because M, K, and O cannot stock aisle 9.
• The template with MKM in 5-6-7 is the most restricted, with only two solutions.

Please let me know if that helps. Thanks!

[r miller]

let me add to dave's awesome and detailed reply by reminding you that games with many rules should not intimidate. the more rules, the more restrictive they collectively become, and the fewer placement possibilities will exist. just as we read logical reasoning questions critically, looking for points or premises that we can use more quickly or immediately, you can - and should - do this on logic games, as well. while reviewing the given information, look for specific rules that, perhaps given the context of the game, create highly restricted situations, either by themselves, or, perhaps more likely, in combination with other rules. (i like to say these are often the last one or ones on list, but every time i start at the end, it turns out to be one of the others, lol!) so, read critically - you are looking for information that will help you resolve the issue.

work quickly, but work methodically. you will find what you are looking for. of course the only question is, with practice, how quickly you will learn to do so.

good luck!

[SherryZ]

Hi there, thank you for your help!

I have read another student's question about this game as well as the response. However I don't understand one sentence of the response: "because O and L must stock aisles behind M, the MKM block cannot be placed on aisle 8 or 9. "

Based on Rule 7, O's aisle is numbered higher than either of K's aisles, and lower than at least one of the L's. So I think O and L must stock aisles behind K instead of M, right?? The sequence would be K in front of O in front of L.

Please correct me if I make mistake. Thank you very much!

---Sherry

[Dave Killoran]

Hi Sherry,

Keep this rule in mind: "Kurt stocks the only aisle between the two aisles Manny stocks." That creates an MKM block, meaning that L and O cannot be immediately next to K, and must be behind M as well.

Please let me know if that helps. Thanks!