- Fri Mar 22, 2019 7:11 pm
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.
Adam M. Tyson
PowerScore LSAT, GRE, ACT and SAT Instructor
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