Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination, Numerical Distribution game.

Because the five tasks (F, W, T, S, and P) must be done in order, you must use the tasks as the base of the game, and show the seven workers (G, H, I, K, L, M, and O) available above each task. According to the information in the rules, only the following people could complete each of the listed tasks:

J00_Game_#4_setup_diagram 1.png

While the above diagram lends a Basic Linear aspect to the game, the number of days it takes to complete the partition adds a Grouping element. The game scenario and second rule establish that the workers must install the partition in either two or three days. Accordingly, the rules allow for several different Numerical Distributions of tasks-to-days:

J00_Game_#4_setup_diagram 2.png

A 1-1-3 or a 1-4 fixed distribution is impossible since T and P are done on different days. A 3-2 distribution is possible since the five tasks must be done in at most three days. Even though the first rule states that “At least one task is done each day,” this allows for a situation wherein the partition completion takes two days and three tasks are done the first day and two tasks are done the second day. As further support, note question #22, which begins, “If the installation takes three days…” The first rule about at least one task per each rules out a distribution such as 3-0-2.

Thus, with the above information we have enough information to attack the questions, but note that this is clearly an unconventional game.

[jei]

hi, newbie here. i am wrestling for the past few days with this question from the june 2000 LSAT, section 1, questions 19-23 (about a crew of five workers installing partitions) and now must petition brighter minds for help. i have to solve the game using brute force, enumering every possibility in every option in every question, but while this is perhaps how Q.19 and 21 are supposed to be tackled, i think other people must have smarter and much less time-consuming way to deal with the other questions.

thanks in advance

[Adam Tyson]

Weclome aboard, jei! That's a fun game you're working on, although it may not seem like it when it's tying you up in knots and slowing you down. Once you crack the key, it becomes much easier.

Why don't you start by sharing with us what your setup looks like, and then we can go from there?

Adam

[jei]

my setup: FWTSP

G: T
H:S,P
I: F,P
K: F,S
L: W,T
M:S
O:W,P

Since the tasked must be done in an order, at least one task is one each day, and T and P must done on different days, there are three possibilities:

3 days total:

(1) T on the 2nd, P and S on the 3rd, while F,W could be either on 1st or 2nd

(2) FWT on the 1st, S on the 2nd, P on the 3rd

2 days total:
FWT on the 1st, SP on the 2nd.

My setup was able to solve each questions except 19 and 21, since the two questions are concerned about workers instead of tasks. Are there any easier ways to solve 19 and 21? Thanks a lot!

[Adam Tyson]

Looks like you have a good handle on it, but your setup is missing one thing, and it is the workers. Since you have the order of the tasks already, imagine that instead of those letters FWTSP, they were numbers, 12345. What approach would you take on a linear game? Not laws, perhaps, split options and dual options, all those things we talk about in the lessons on linear games, right?

In this case, they gave you all the possible placements for each worker (and the workers are your variables here, along with the days, while the tasks are the ordered base). So, who could go first (in the space for F)? Only I and K, so that's a dual option above F. Follow through with that, and you should start to see how to tackle those questions that deal with which workers could work which days or with whom.

Give that a shot and let us know how it goes!

Adam

[Adam Tyson]

A student asked this question in another thread:

in hwk 7 for the on demand books i'm having trouble with the setup and explanation for game #3 for june 2000 on pg. 7-86.

firstly, i don't understand how they got the task-to-days numerical distribution found in the game explanation
secondly, I'm confused on how to diagram the day component

If ya'll could diagram the game and explain it in a different way than the book does i'd be really grateful.

Faith

Just to be clear, that's Game 3 in the homework for lesson 7, but it's game 4 on the actual test. We'll provide an answer here!

[Adam Tyson]

Hey Faith, let me see if I can help! The tasks are FWTSP, in that order, and they can be done in the course of either 2 days or else 3 days. Why not one day? Because the rules tell us that T and P cannot be the same day as each other. So, what are the options for tasks done per day? Let's run through them:

If the tasks are done in two days, the break between day 1 and day 2 has to be after Taping has been completed. That way we can be sure that Taping and Priming are on different days. So, we could do it this way:

Day 1: FWTS; Day 2: P (a 4-1 distribution of tasks to days)
Day 1: FWT; Day 2: SP (a 3-2 distribution)

So far, so good. Now, what if we take 3 days to do the job? We still need at least one break between T and P somewhere. Let's start with as many tasks on Day 1 as possible:

Day 1: FWT; Day 2: S; Day 3: P (that's a fixed 3-1-1 distribution, three tasks on the first day and one task per day for each of the other two days)

Now let's scale back Day 1 to just 2 tasks, which gives us these options:

Day 1: FW; Day 2: TS; Day 3: P (a fixed 2-2-1 distribution)
Day 1: FW; Day 2: T; Day 3: SP (a fixed distribution of 2-1-2)

Finally, what if there is only one task on Day 1? Here's what we could get:

Day 1: F; Day 2: WTS; Day 3: P (1-3-1)
Day 1: F; Day 2: WT; Day 3: SP (1-2-2)

That's it, there are no other ways to slice this one up and still keep T and P on different days. Now, notice that there are three different fixed variations where two days have two tasks each and one day has just one task. There's a 2-2-1, a 2-1-2, and a 1-2-2. That's why in the book we just lump them together as a single "unfixed" distribution of 1-2-2. That just means that there is more than one way to use that combination of numbers for tasks per day.

Why didn't we write out all 7 fixed distributions? Because that takes a lot of time! Also, there are only 5 questions, so 7 distributions are overkill. Instead, I would advise just looking at the unfixed distributions. How can I divide 5 things among 2 days, with at least one task per day? It's either 4-1 or else 3-2, unfixed (except they actually do turn out to be fixed, in this case). How do I do 5 into 3, with at least one per day? 3-1-1 or 2-2-1, both unfixed. 4 distributions, 5 questions - that's more like it!

Now, how do we diagram the day component? We could do it as shown in the book, with either two or three columns to represent the days and the appropriate number of slots for the number of tasks done each day, or else we could try keeping the five tasks in a straight line and putting breaks between them. For example, question 20 establishes a 2-1-2 fixed distribution just in the way the question is asked (two people working on the first day and the same two working again on the third day), and that could be drawn like this:

_ _ | _ | _ _
FW T SP

From there it's just a question of who can do which of those tasks!

I hope that makes it clearer for you! Give that a try and see if it works out, and let us know if you need further help with it.

[Tajadas]

I used the days, 1, 2, and 3, rather than the order of tasks as a base. I hesitated when I decided to do this, but I thought it'd be easier to keep track of the days that way. I got everything right, but I'm sure it took much longer than if I had used the tasks as a base. How was I supposed to tell I was supposed to use the tasks as a base since both tasks and days have orders?

[Adam Tyson]

The problem with the days as the base, Tajadas, is that we don't know how many days will be used. It could be just two days! I suppose you could set up a three day base and then have some solutions where there are no tasks on day 3, but since the tasks have an absolute, fixed order to them they make a more certain, reliable base than the days.

It's an unusual game to have two different orders layered together, and that makes this a great game to study!

[sofcu23]

Hi,

I'm really having trouble understanding how the partition could be installed in two days. I know the stimulus says "at most", but then the first rule says that "at least one task is done each day"

I'm also confused with the first post explanation where it states that "A 3-2 distribution is possible since the five tasks must be done in at most three days.", but then that "the first rule about at least one task per each rules out a distribution such as 3-0-2."

These seem to contradict each other? I'm not sure how we can assume that two days is a possibility if it clearly states that at least one task is done each day.

Thanks in advance