Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Unbalanced: Overloaded, Numerical Distribution game.

The game scenario establishes that there are four areas for charitable grants, and one or more grants are awarded each quarter. The first two rules then establish that a grant is awarded in each area, and that no more than six grants are awarded. With the information from the fourth rule that exactly two medical grants are awarded, the base diagram for this game appears as:

PT57-Jun2009_LGE-G4_srd1.png

The scenario and first two rules also establish two Numerical Distributions of numbers of grants to the four areas (not quarters):

PT57-Jun2009_LGE-G4_srd2.png

When the five or six grants are assigned to the four quarters, the distributions change:

PT57-Jun2009_LGE-G4_srd3.png

The third rule establishes that grants in the same area cannot be awarded consecutively or in the same quarter. Instead of showing a not-block for each area, we will use “G” to represent a grant area, and create GG not-blocks to represent all eight relationships:

PT57-Jun2009_LGE-G4_srd4.png

Note that, because of this rule, the two M grants will be awarded in 1-3, 2-4, or 1-4.

The fifth rule establishes that W is awarded a grant in the second quarter. From the third rule, no other W grant can be awarded in the first, second, or third quarters:

PT57-Jun2009_LGE-G4_srd5.png

Other than the above information, there are no further setup elements to be created.

[cmeggs]

Hello,

I ran into trouble with this question because I ran out of time... Most of the questions are of a global nature. Here is my set up:

m,t, w, y

__ __ __ __
__ __ __ __
__ w __ __
1 2 3 4

between 5-6 awards
at least 1 grant in each area
no consec or same quarter
M2

This was as far as I got set up wise, but with so many global questions I ended up having to test a lot of answer choices and running out of time.

I am wondering if I missed some obvious inferences, or what a good strategy would be like for a game like this.

Thanks!
Caitlin

[Jon Denning]

Hey Caitlin - thanks for the question. I don't think you've missed anything too major. To add to your diagram, I'd likely also include not laws for W in 1 and 3, and show the three possible distributions with 5 or 6 grants: 2-1-1-1 (5), 3-1-1-1 (6), or 2-2-1-1 (6).

Aside, from that, I think it's just a matter of really focusing on the numbers/distributions, avoiding consecutive grants and making sure you have 2 Ms.

Take 19: D is impossible because you'd have 2 M, 2 W, and 2 Y...violates distribution possibilities.

Or 20: E cannot happen because you would have that WY block either in 2 and then Y in 3, or the WY block in 3 and then W in 2. Consecutive grant violation.

21 is purely from the distribution 2-1-1-1 (5 total, M M T W Y), where only B could be true: no M or W or Y first quarter means first quarter T, second quarter MW, third quarter Y, fourth quarter M. Answers A and C make something other than M go twice, and D and E force M into both 3 and 4.

And for 22, if D were to happen then your two Ms would be in 2 and 3, which is a violation.


So tricky game without a lot of upfront inferences, but certainly beatable. Hope that helps!

Jon

[SherryZ]

HI there, good evening and thank you for your help!

June 2009 LSAT, Sec 1 LG, Game 4:

I set up this game based on the rule 4 "2 medical services grants are awarded" as following:

Possibility 1 (When M = 1&3)
M W M _
1 2 3 4

Possibility 2 (When M = 1&4)
M W _ M

Possibility 3 (When M = 2&4)
_ W&M _ M
1 2 3 4

But I don't think this method is right. Could you tell me the most efficient and accurate way to set up this game. Also, could you tell me what inferences I can generate from the conditions?

Thank you very much!

---Sherry

[KelseyWoods]

Hi Sherry!

It's not a terrible idea to show those Templates, but placing M doesn't really tell you where anything else goes. Generally, you should use Templates when placing a variable in a certain location, forces other variables in to certain locations. But your Templates do show you the three options for how M can be arranged and I think seeing that could be helpful.

There aren't a ton of inferences with this game. Since W is 2nd and you can't have consecutive areas, that means that W can't be in 1 or 3.

Numerical Distribution is important to consider with this game. Rule 2 tells us we have a max of 6 grants. Since we have to have at least one grant in each area and there are two in medical services, that means we will have 5 or 6 grants. So the possible distributions for those grants into the days are:

3 - 1 - 1 - 1
2 - 2 - 1 - 1
2 - 1 - 1 - 1

This means that the max number of grants you could have in one quarter is 3 (top distribution) and the max number of quarters you could have with more than one grant is 2 (middle distribution).

You could also do the distribution for the number of grants into the different areas. Since there are exactly 2 medical services grants, the possible distributions would be:

2 - 2 - 1 - 1
2 - 1 - 1 - 1

Keeping track of numerical distributions can help you in the questions with this game.

Hope this helps!

Best,
Kelsey

[jk11]

Hello!

I don't understand why on #23, the correct answer is E. This is because I don't understand the difference between 3 grants being in the first quarter vs. 3 grants being in the second. I know I'm missing something here. Could you help me see the difference?

Thanks!

[James Finch]

Hi JK,

Good job narrowing down the contenders to just the two choices! At that point, it makes sense to game out both. Since we know the W is in the 2 column, then if we put 3 in the 1 they have to be one each of the remaining three variables (M,T,Y). That leaves one more M that can go either in the 3 or 4 spot, plus possibly T or Y in the 3 or 4 or W in the 4. So we can't fully determine the placement by stacking up the 1 column.

However, if we put the M-T-Y in the 3 column, then the rule about not having variables in consecutive columns comes into play and we're left with an M that is forced into the 1 column; if there is a 6th grant awarded, then we would immediately know where it was too (T or Y in 1, W in 4).

Hope this clears things up!

[jwheeler]

#23 addition... And actually for E, we know that W is forced into the 4th quarter. The rules tell us that every quarter has to have at least 1 grant given, so since M,Y,T are all in the 3rd, we know that W must fill the spot in the 4th. That part stumped me at first because I forgot the rule against adjacency, so I thought it was too vague. A visit back to the rule set helped clear it up.

[Malila Robinson]

Hi jwheeler,
That was a tough question! it sounds like you managed to meet it head on! Great job!
-Malila

[tomthomse@gmail.com]

If anyone took this on the LSAC Lawhub site, they credited D as correct on 22, when it should be E!