Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced, Identify the Templates game.

The first sentence of the game establishes a linear scenario of seven consecutive spaces:

PT66_J12_Game_#2_setup_diagram 1.png

The second sentence establishes that seven business will fill these spaces in a one-to-one relationship. The seven variables feature an unusual feature: instead of seven wholly separate variables, in this game there are two restaurants. While the initial inclination may be to simply label those as R and R, because of the linear factor the better approach is to label them as R1 and R2. This would then allow you to smoothly handle any rule that linked a variable to the first appearance of R (and while this does not occur in this game, this type of rule has appeared in other games, and you want to be consistent in how you represent the variables from game to game in order to best address any type of rule you encounter). Consequently, the variable set for this game appears as:

PT66_J12_Game_#2_setup_diagram 2.png

The first rule of the game presents two mutually exclusive scenarios. Thus, the best response to the first rule is to create two separate templates:

• Template #1: P in space 1, and R in space 7

PT66_J12_Game_#2_setup_diagram 3.png

In this template, P is in space 1 and thus an R must be in space 7. Because space 7 is the last space, the R must be the second R (R2).

• Template #2: P in space 7, and R in space 1

PT66_J12_Game_#2_setup_diagram 4.png

In this template, P is in space 7 and thus an R must be in space 1. Because space 1 is the first space, the R must be the first R (R1).

Because the first rule helpfully creates two templates, as we consider each subsequent rule, we will address them within the context of each template.

The second rule creates a minimum split block for the two Rs:

PT66_J12_Game_#2_setup_diagram 5.png

This block creates two R Not Laws on each template:

• Template #1: P in space 1, and R in space 7

PT66_J12_Game_#2_setup_diagram 6.png

• Template #2: P in space 7, and R in space 1

PT66_J12_Game_#2_setup_diagram 7.png

The third rule creates another block, one that establishes that O or V is always next to P:

PT66_J12_Game_#2_setup_diagram 8.png

Of course, since this block rotates, it can be shown with a circle:

PT66_J12_Game_#2_setup_diagram 9.png

While this rule initially seems as if it may be troublesome because it contains four possibilities, the placement of P is already established, so this rule is easy to capture in the two templates:

• Template #1: P in space 1, and R in space 7

PT66_J12_Game_#2_setup_diagram 10.png

• Template #2: P in space 7, and R in space 1

PT66_J12_Game_#2_setup_diagram 11.png

Note that in each template, the unassigned R is restricted to just two placement options.

The fourth rule creates a rotating not-block between T and V:

PT66_J12_Game_#2_setup_diagram 12.png

Of course, since this not-block rotates, it can be shown with a circle:

PT66_J12_Game_#2_setup_diagram 13.png

Note that no Not Laws can be drawn from this rule until one of the variables in the not-block is placed. However, because V also appears in the third rule, the connection of those two rules should be tracked throughout the game.

Combining all of the previous information results in the final setup for this game:

PT66_J12_Game_#2_setup_diagram 14.png

PT66_J12_Game_#2_setup_diagram 15.png

Note that the two templates are functionally identical. That is, adjusting for the fact that they are reversed, the two templates are mirror images of each other. This occurs because each of the rules allows for rotation in the placement of the affected variables. Thus, when an occurrence is impossible (or possible) in one template, then it will be impossible (or possible) in the other template (with the spaces flipped). For example, assume S could not be in space 3 in Template #1 (that’s not the case, but assume it is for a moment). If this were true, then S could not be in space 5 in Template #2. Or, if T could not be in space 2 in Template 2, then T could not be in space 6 in Template #1. This feature does not play a major role in the game, but it is useful in helping to solve questions such as #9.

[Dajpol]

My setup for this game was pretty bare and so this game then took me too long to complete. What's the plan of attack for this one?

Thanks!

[Nikki Siclunov]

Hi Dajpol,

I approached this game with templates, as the first rule establishes two mutually exclusive scenarios:

• Template #1: P is in 1, R is in 7
  
  P __ __ __ __ __ R
  
  Template #2: P is in 7, R is in 1
  
  R __ __ __ __ __ P

The second rule generates two R-Not Laws in each template, because the two R's must be separated by at least two other variables.

The third rule creates a rotating block: P O/V or else O/V P. Since the placement of P is already established in each template, we can represent the implications of the third rule as follows:

• Template #1: P is in 1, R is in 7
  
  P O/V __ __ __ __ R
  
  Template #2: P is in 7, R is in 1
  
  R __ __ __ __ O/V P

(Note that in each template, the unassigned R is restricted to just two placement options.)

The fourth rule creates a rotating not-block between T and V. No Not-Laws can be drawn from this rule.

Note that the two templates are functionally identical. That is, adjusting for the fact that they are reversed, the two templates are mirror images of each other. This occurs because each of the rules allows for rotation in the placement of the affected variables. Thus, when an occurrence is impossible (or possible) in one template, then it will be impossible (or possible) in the other template (with the spaces flipped). For example, assume S could not be in space 3 in Template #1 (that’s not the case, but assume it is for a moment). If this were true, then S could not be in space 5 in Template #2. Or, if T could not be in space 2 in Template 2, then T could not be in space 6 in Template #1. This feature does not play a major role in the game, but it is useful in helping to solve questions such as #9.

Hope this gives you a place to start!

Thanks,

[Dajpol]

Thanks!

[glasann]

As I did the questions and saw more about how the came worked, I realized I should have templated this. However, in the middle of the timed section, it was kind of too late before I made that realization. I redid it afterwards and, sure enough, it was so much easier with the templates.

How could I have avoided this and realized immediately that I should be templating this when I first did the set up?

Thank you

[Adam Tyson]

Whenever a game gives you two mutually exclusive options, you should at least consider whether a template approach would be worthwhile, glasann. I at least think about templates for pretty much every game, even if it's just to think to myself "nah, this one isn't going to be a good template game." Make that mental inquiry a part of your standard attack on every game so that you never overlook the option to do so. My mental checklist looks something like this:

1) Is there order here?
2) What should my base look like?
3) What's happening with the numbers - are we balanced, unbalanced, etc.?
4) Does this look like maybe I can do templates?

And from there it's all about connecting the rules, noting the randoms, making obvious inferences, digging a little for some less-obvious inferences, and getting on to the questions without staring at it for too long.

Templates may not always be an obvious choice, and they are often not a good choice, but they should always be on your mind! Add that to your process and you won't miss these opportunities.

[glasann]

That is helpful. Thank you, Adam.