Which one of the following could be the assignment of employees to information booths?

Sharon on February 16 at 01:17AM

Setup

Can you show me the set up of this game please

1 Reply

on February 16 at 08:44PM

Hello @sharonk0912,

Of course!

People: F G H K L M (6)

Three booths: O R V.
Each booth must have at least one person assigned to it.

Pay very close attention to our first rule, which I express with R>V. This rule gives us our distribution, which makes it very important. How many ways could the retailer booth have more people than the visitor booth? The retail booth must have at least 2 spots. The visitor booth cannot have more than 2. (I've placed some variables, but just pay attention to the number of people at each booth for now.) It goes 3-2-1, 1-3-2, 2-3-1, or 1-4-1

1.
O: F K L
R: G M
V: H

2.
O _
R _ _ _
V _ _

3.
O _ _
R G M _
V H/L

4.
O _
R G M _ _
V H/L

There are 4 possible distributions. Because there are only 4, it is worth my time to write them all out. I usually won't do more than 4, but that's just my personal rule. You can see that I've filled some of them in. I'll explain why.

Let's continue with our other rules.
V: not F and not K
O: not G and not H
GM are together.

A key inference: Because GM must be together, M also cannot be at O. We have now eliminated three people from the organizers booth, leaving only F K L. This is how I was able to solve diagram 1 completely. If a question tells us that O has three people, we know exactly which diagram to use.

I have also placed my GM block where I could. In diagrams 3 and 4, this leaves only H or L as possibilities to fill the spot at V booth. (This is because F, K, G, M cannot go there, leaving only H and L).

Notice that diagram 2 still has a lot of uncertainty. GM could go with either V or R.

This may seem like it has taken forever. But, if you do all of this, you will see how quickly you can breeze through the questions.

For example, look at question 12. Neither Hal nor Laura is assigned to the visitors booth. Immediately, that tells me that I must be using diagram 2. With F, K, H, and L eliminated from V, I know that GM has to be there. This is the correct answer.

How about question 9? In which diagram are there more organizers than retailers? Only diagram 1, which is completely solved. I answered this question before I ever saw it. That is the magic of making inferences and diagramming them.

Do you see how important it is to understand which distributions are possible? Next time you see a rule like the first one, you will know what to do.