Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

The game scenario indicates that six service appointments will be scheduled for six consecutive days, exactly one per day, leading to the following Basic Linear setup:

D10_game #1_setup_diagram 1.png

From a quick analysis standpoint, this seems like a reasonable first game to attempt on the test.

The first rule establishes a basic sequence:

• W L

This rule leads to two Not Laws, one for W, which cannot be last, and one for L, which cannot be first:

D10_game #1_setup_diagram 2.png

The second rule also creates a conditional relationship, albeit one that is more complex than the relationship in the first rule:

D10_game #1_setup_diagram 3.png

This rule leads to four Not Laws: G and S cannot be scheduled for the first day, and P cannot be scheduled for the fifth or sixth days:

D10_game #1_setup_diagram 4.png

With the first two rules generating three Not Laws on the first day, we can infer that only P, T, or W can be scheduled for the first appointment:

D10_game #1_setup_diagram 5.png

The third rule establishes that G, S, and T cannot be scheduled for the second and third days, leading to six additional Not Laws:

D10_game #1_setup_diagram 6.png

Of course, with those three services eliminated from the second and third days, only L, P, and W can possibly be scheduled for those two days:

D10_game #1_setup_diagram 7.png

The third rule is extremely powerful, and there are two inferences that follow from this rule:

• 1. If one of L, P, or W is scheduled for a day other than the second or third day, then the remaining two services must be scheduled for the second and third days. For example, if W is scheduled for the first day, then L and P—not necessarily in that order—must be scheduled for the second and third days.
  
  2. From the second rule G and S cannot be scheduled for the first day, and from the third rule G and S cannot be scheduled for the second and third days. Thus, G and S must be scheduled for days four, five, or six. More on this inference in a moment.

The fourth and final rule establishes that T cannot be scheduled for the sixth day, which leads to another Not Law on day six:

D10_game #1_setup_diagram 8.png

With three Not Laws now present on the sixth day, we can infer that only G, L, or S can be scheduled for the sixth day:

D10_game #1_setup_diagram 9.png

An analysis of the diagram above shows that the game is composed of two interlocking systems:

• 1. Only T, L, P, and W can be scheduled for the first three days.
  
  With only four services available to fill the first three days, if any one of T, L, P, and W is scheduled for the last three days, then the remaining three must be scheduled for the first three days, in accordance with the restrictions already shown on the diagram. This is incredibly limiting and has a major effect on the game.
  
  Note that because only one of the three variables can be removed, that variable cannot be W, because then L would also be removed due to the first rule. Thus, W cannot be fourth or fifth, and that will be shown with Not Laws on the main diagram below.
  
  2. G and S must be scheduled for the last three days.
  
  As established previously, G and S must be scheduled for the last three days. Thus, when another service aside from G and S is scheduled for the fourth, fifth, or sixth day, then G and S will fill the remaining two days. So, for example, if L is scheduled for the fourth day, then G and S—not necessarily in that order—must be scheduled for days five and six. Of course, because that other service must be T, L, P, or W, when one of those four is scheduled in the last three days, the composition (but not order) of the services in first three days and the last three days is fully determined.

The two points above will be shown “floating above” the main base of the diagram, leading to the final diagram for the game:

D10_game #1_setup_diagram 10.png

Thus, although this game appears to be relatively simple, there are some complex—and quite helpful—interactions occurring among the rules.

[jmcbee12]

Hi I messed up on setting this game up and I was wondering if you could help me with how it looks?

Thanks

[Stephanie Oswalt]

Dear Jmcbee,

Thanks for your question. Generally speaking, we need a bit more input from you before we delve into a discussion of a particular logic game. Ultimately, it won't be us who are taking the test; it's you! Our goal is to help you cultivate the analytical ability to approach these games on your own, which is why you need to help us help you first.

Here's what I'd like you to do:

1. Describe your approach to the setup. Were you able to determine what type of game it is? What the variable sets are?

2. Were you able to diagram any of the rules, or make any inferences?

I am confident that you will get more out of our help if we start with an understanding of how you approached the game and what you found difficult about it.

Thanks!

Stephanie

[Jgalkin]

Hi,
Can you please demonstrate the complete set up for this game?
While I did it pretty well on my own, I would like to have the official way for comparison.
Thank you,
Jeffrey

[Stephanie Oswalt]

Hi Jeffrey!

Thanks for the question. We have posted the administrator setup/explanation above.

Please let us know if you have any additional questions.

Thanks!

[deck1134]

Hello,

I missed the inference that W cannot be in 4 or 5. The explanation says that since you must choose two of the three then W must be there. What about the order T L P in 1, 2, and 3, respectively. Why does that force W out? How do you make that inference faster? What am I missing?

[Adam Tyson]

You're overlooking the first rule, Deck - W must be before L! If W was scheduled any later than third, with L after it, then we would be unable to fill the second and third slots. Only P would be available to fill those two slots.

When in doubt, run through the rules! Use them like a checklist, if that helps. Try a hypothetical, with W at, let's say, 5. You'll learn pretty quickly that it won't work, and make that inference about W.

Give it another look, and good luck!

[Kelly R]

Hi PS,

For rule-substitution questions, if an answer choice violates a viable hypothetical from an earlier question in the game, it can be eliminated, correct? Thanks.

[Adam Tyson]

Correct, Kelly. If the question is asking which answer choice would have the same effect as the rule that is being replaced, then the new rule has to work perfectly within every viable hypothetical solutions you may have diagrammed along the way. I like to think of these questions as asking "which of these answers would result in an identical diagram?" When approached that way, with an eye towards how you would diagram each answer, these become much easier!

[frk215]

Would it be a good move to create three templates based on where t can be placed here? I did that and it helped a lot but i also took too long on the first game. I wonder if that's because I needed to move through the questions more confidently/quickly or whether I should have just not created those templates. Thanks for the help!