Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario creates the following initial diagram:

PT57-Jun2009_LGE-G2_srd1.png

While normally there is no need to number each variable, in this case, the first rule establishes that the first day an actor auditions is important (and in this sense, the game is similar to the Cookie Batches game that appeared on the December 2003 LSAT). Thus, the variable set should appear as:

PT57-Jun2009_LGE-G2_srd2.png

The six auditions must be spread over four days, with a minimum of one audition per day. This creates a Numerical Distribution of six auditions into four days. Let us first examine the minimums present:

PT57-Jun2009_LGE-G2_srd3.png

Thus, there are two extra auditions to be distributed across the days. There are only two possible ways to distribute the two auditions:

PT57-Jun2009_LGE-G2_srd4.png

Thus, under the 3-1-1-1 distribution, there is one day with three auditions and three days with one audition. Under the 2-2-1-1, there are two days with two auditions and two days with one audition.

The first rule should be diagrammed as:

PT57-Jun2009_LGE-G2_srd5.png

This sequence rules out R (both R1 and R2) from appearing on Wednesday. And, of course, if R1 cannot audition on Wednesday, R2 cannot audition on Thursday. In addition, O1 cannot audition on Friday as this would force R1 to audition on Saturday (leaving no day for O2). These Not Laws appear as:

PT57-Jun2009_LGE-G2_srd6.png

Additional Not Laws could also be shown on Wednesday (for all the “2” variables) and on Saturday (for all the “1” variables) but that seems redundant due to the relative obviousness of each.

The second rule establishes a GR block:

PT57-Jun2009_LGE-G2_srd7.png

Because R1 cannot audition on Wednesday, this block cannot appear on Wednesday. However, G1 could still audition on Wednesday, with G2 later auditioning on the same day as R.

The third rule connects Thursday and Saturday:

PT57-Jun2009_LGE-G2_srd8.png

Thus, one actor has his or her first audition on Thursday, and a second audition on Saturday. Consequently, there cannot be three auditions on Wednesday (because at least one “1” audition must be on Thursday, and no second auditions can occur on Wednesday), and there cannot be three auditions on Friday (for the same reason: because one actor is fully booked on Thursday and Saturday according to the third rule).

[stsai]

Q6-11. 3 actors--Gombrich, Otto, Raines audition for parts...

From the back of the bible, I learned that this is a Advanced Linear, Unbalanced-Overloaded, # Distribution game, and is very difficult for me to set up.
Though I know to mark the persons as GGOORR and XX (2 empty spots) for the 6 into 8 distribution. I only made it to Q7, but got both Q6 and 7 wrong.
Could someone please show the setup for this game?
Thanks!

[Dave Killoran]

Hi Stsai,

The game you reference is actually from June 2009, not June 2008. After glancing at your comments, I think your error is in assuming that there are exactly two auditions each day (and thus, with only six actor auditions, there are two X variables for empty spots). However, because there is no specification that there are exactly two auditions per day, there are no "empty spots" to fill.

Instead, look at this game as the six auditions going over the four days, with a minimum of one audition each day. This leads to two unfixed numerical distributions of the six auditions to the four days: 3-1-1-1 and 2-2-1-1.

Try the game again from that perspective and see if you don't find it to be easier.

Thanks!

[stsai]

I see. But the next step I could think of is to make templates---which would be 7 of them (1-3-1-1, 1-1-3-1, 1-1-1-3; 1-1-2-2, 1-2-1-2, 1-2-2-1, 2-2-1-1)---so this seems a bit inefficient. Is there another way to tackle this numerical distribution? Not laws? (But I can't think of a good way to make Not laws with this much uncertainty...)
Thanks!

[Dave Killoran]

You could do that, but that's not the direction I'd go because there are still plenty of options within each. Plus, with any of the 3-1-1-1 distributions, you know that GR is among the three, so that really makes those limited. So just considering the situation beforehand, we already have a lot of useful info before having to take the time to make templates.

Then, take a look at the questions:

#6 is a List question, so pretty easy.
#7 + #11 are Local questions, so that extra info helps limit the possibilities.

So, we have three questions where we likely wouldn't need the possibilities (The remaining Global questions actually aren't that tough either; for example, #8 is a question that trades directly on the first rule, and #9 has two answers eliminated by the answer to #6 and the question stem in #7)

Once you have the distributions and have considered the three rules, you actually have a lot of info--enough in my opinion not to need to take the time to write out templates. Just get into the questions and start attacking.

Thanks!

[adlindsey]

The phrase on the scenario, "on each of these days at least one of the actors auditions for parts." What does that mean? I looked at another explanation and it was stated that it meant some days could be empty. I interpreted it as each day must have a least one actor.

[Adam Tyson]

That definitely means there cannot be any empty days, adlindsey! Your interpretation is correct. I hope the other explanation you saw wasn't one of ours? If it was, please tell us where you found that, either in one of our books or in our online materials, so we can proofread it and make any needed corrections.

Thanks!

[adlindsey]

It was a different company.

[Adam Tyson]

Phew! Good to know. Stick with us, we won't steer you wrong like that!

[bella243]

Could someone please show the best way to diagram this game? The global list question shows actors as the base; I used weekdays as the base but still found the set up process challenging.

Thanks.