Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Balanced Advanced Linear game.

The three floors are chosen as a vertical base, and then slots for each car choice are provided. Because there are three choices—F or S, N or U, and P or R—there are three slots for each floor.

The second and third rules are negative conditional rules that establish that U and R cannot be on the same floor, and that R and S cannot be on the same floor. This leads to several key deductions:

• U P R N R F S P

The key deductions above follow from the two-value system that exists for each of the three choices for cars on each floor. For example, since the cars on each floor must be either family cars or sports cars, and cannot be both, if family cars are not included on a floor then that floor must include sports cars. The same holds true for the new or used car choice and for the production or research model choice. This simple fact yields some powerful inferences when combined with the second and third rules. For example, the second rule states that the exhibition includes no used research models. Thus if the cars on a floor are used, they are not research models. This can be represented as:

• U R

However, if a car is not a research model then it must be a production model and thus the rule can be more effectively diagrammed as:

• U P

From this inference it follows that since the third floor of the exhibition has used cars, the third floor must also have production models, and this inference is shown on the main diagram.

Continuing on, the contrapositive of U P is:

• P U

But, again applying the two-value system, if a car is not a production model, then it must be a research model which cannot be used, and if it is not used, then it must be new, which can be diagrammed as:

• R N

The same type of reasoning can also be applied to the third rule which involves research models and sports cars.

This set of inferences, which follow from the two negative conditional rules and the two-value system, are critical to solving this game quickly.

[EsquireGirl]

Hi,

The set up for the advanced games are stumping me a bit. Can you show what the set up is for this game?

When looking over some of the other explanations of the advanced games, I have actually understood most of the relationships, but without a good set up, it's a struggle.

Thanks,

[EsquireGirl]

Hi,

So I read another post where you want to see or get an explanation of our set up before you just give it to us. Understood. So here is my set up to the automobile show game:


Cars: F, S 3_________ F + S ----> F----------S
Type: N, U 4_________ R subscript u w/a line through it next to R subscript s w/a line through it
Model: P, R 5_________

Thanks,

PS - After I submit, the set up gets a bit crunched up.

[Adam Tyson]

Yeah, Esquire, it can be tough recreating a setup in this forum. One of these days I will get my colleagues to teach me how to do it better than I have been!

Here's how to approach this game: ask yourself what it is that you are trying to figure out. For me, the answer to that question is something like "for each floor of the building, what types of cars are being displayed?" That approach, where I have said "for each floor", tells me that the floors are the base in this game. Because we are dealing with floors of a building, it makes sense to set those up vertically, just like a real building. Something like this:

3. ___ ___ ___
2. ___ ___ ___
1. ___ ___ ___

I've included three slots on each floor, because on each floor I am going to be assigning three different characteristics to each car. One column is for F/S (Family or Sports); another is for U/N (used or new); a third column is for R/P (research or production). I would label my first column as being for F/S, my second is for N/U, and my third is for P/R. I would put those labels at the bottom of each column, like this:

3. ___ ___ ___
2. ___ ___ ___
1. ___ ___ ___
F/S N/U P/R

(the order in which you label these really doesn't matter - I chose this order only because that is the order in which they were presented in the scenario).

This setup makes good sense not only because of the way it matches what we are trying to find out about the game, but also because in a holistic sense it matches up with reality in a visually appealing way. It looks like a building with three floors with different kinds of cars on each floor. For example, maybe the bottom floor has family cars that are new and production,which I could represent with the letters FNP. I can place FNP in the three slots on row 1, and that tells me that floor 1 has cars that fit those three criteria.

Play around with that and see if the game makes more sense to you now. For future grouping games, ask yourself that question - what am I trying to figure out here? - and answer it in the format of "for each ___ I want to know ___". The first blank will be your groups, the second will identify the variables being placed in those groups.

For each of your questions, I want to be able to provide a useful answer!

[Kgorham]

Is floor three not assumed to be S because we don’t know whether there are any sports cars?

In other words, is a not law for F next to floor three wrong because the rule is a conditional statement?

[Adam Tyson]

Correct, Kgorham! These rules allow for the possibility of family cars on all three floors. Well done!

[andbzav@gmail.com]

Should the second sentence in the scenario be taken to mean that each floor has cars that are all some combination of the three descriptions - new or used, family or sports, research or production - for example, all the cars on a floor could be new family production cars (not taking into account the rules here)? Seeking further clarification of the second sentence.

Thank you

[Jeremy Press]

Hi andbzav,

Yes, you've got the proper interpretation of the second sentence of the scenario! The final "and" in that sentence clarifies that all three "either-or" dichotomies are applicable to all cars on the floor. Thus, all cars on the floor have the same combination of the three different categories of characteristics: newness [new OR used], style [family OR sports], AND development status [production OR research].

I hope this helps!

Jeremy

[andbzav@gmail.com]

Helps a lot. Thank you!

[TIFFANY_L]

Hello, wondering why #18 and #19 were not diagrammed the same way if the stimulus in both questions were the same? Could they have both been diagrammed the same way?

#18) "If all the new cars in the exhibition are research models..."

diagrammed as: N --> R
(one direction arrow)

#19) "If all the production models in the exhibition are used..."

diagrammed as: P <--> U
(double arrow)

Thank you!