Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The game scenario and first two rules create an Advanced Linear scenario:

J02_Game_#1_setup_diagram 1.png

The third rule helpfully assigns females to two of the eight wings:

J02_Game_#1_setup_diagram 2.png

The fourth rule indicates that if males are assigned to a wing, the other wing must be assigned females. Operationally, this means that males can never be assigned to both wings of a dormitory, which results in a vertical not-block:

J02_Game_#1_setup_diagram 3.png

The fifth rule is conditional:

• VSM WNM

Of course, if the fifth rule is enacted, and both those wings are assigned males, then by applying the fourth rule, the other wings in those dormitories would be assigned females:

J02_Game_#1_setup_diagram 4.png

Thus, if Veblen South is assigned males, the Veblen and Wisteria dormitories are fully assigned.

This game also contains a two-value system: each dormitory is assigned either male or female students. Thus, if a dormitory does not have male students, then the dormitory must have female students. As is so often the case, the two-value system can be applied to a conditional rule to create greater insight. Consider the contrapositive of the final rule:

• WNM VSM

The same contrapositive reinterpreted by applying the two-value system:

• WNF VSF

This inference is directly tested in question #3.

Another point of restriction in the game is the males. Because males cannot be assigned to both wings of a dormitory, at most males can be assigned to one wing of a dormitory. At the same time, the rules state that there must be exactly three wings with males. Because there are only four dormitories, the situation is restricted, and the following inferences can be drawn:

1. If a dormitory has female students assigned to both wings, then the males must be assigned to one wing in each of the other three dormitories. For example, if Tuscarora South is assigned females (as in question #5), then males must be assigned to Richards South, Veblen North or South, and Wisteria North or South. In question #5, this inference is sufficient to eliminate answer choices (A), (B), and (E). Answer choice (C) can be eliminated by the contrapositive of the final rule, leaving answer choice (D) as correct.

Another way to look at this inference is to assert that only one dormitory can be all-female, and the other three dormitories must each have one male and one female wing.

2. Among any two dormitory pairs, males must always be assigned to at least one wing. For example, with Veblen and Wisteria, at least one of the four wings must always be male.

This inference is directly tested in question #2. With Richards and Tuscarora (only South is relevant since the North wings are assigned to females), at least one must always be male, otherwise there will not be a sufficient number of wings available to house the males. Hence, answer choice (B) is correct.

The final setup to the game appears as follows, but keep in mind the points made in the analysis of the two-value system:

J02_Game_#1_setup_diagram 5.png

After a careful consideration of the rules, the only two active rules are the fourth and fifth rules. Obviously, you should pay close attention to these rules as you work through the questions, and indeed, the interaction of these rules creates several powerful inferences that are tested throughout the game. In fact, the inferences are so powerful that only a limited number of templates exist for this game, and one approach would be to show the three basic templates:


Template #1: Veblen South is male. Two total solutions.
Template #2: Wisteria North is female, Veblen South is female. Four total solutions.
Template #3: Veblen South is female, Wisteria North is male. Three total solutions.


The choice to show the templates is yours because the game can be done quickly with either approach.

[srcline@noctrl.edu]

Hello

I am absolutely confused on how to set this one up. Are the North and South wings the base and vertical with four stacks. I'm lost on this game and its rules.

Thankyou
Sarah

[Clay Cooper]

Hi Sarah,

Thanks for another great question.

The setup should look something like what follows below:

R T V W
_ _ _ _ N
_ _ _ _ S

Now we will fill in each blank with M or F once we know the gender of the students assigned to it. It is not important, really, whether the diagram shown above is executed horizontally (as shown) or vertically (as you mentioned) - it will work either way. I have drawn it horizontally because doing so allows me to draw the North blanks as a row and have that row placed above the row of South blanks; in other words, it seems smart to put North above South, since that is how we will tend to intuitively think about it anyway.

Does that help?

[NegusAlfie]

This seems more like a grouping than a linear game. I am not sure where the linearity comes in to be honest.

[Ryan Twomey]

Hey Negusalfie,

I guess it depends on the definition of linear. I usually think of a linear game as a game where some type of order matters, where I would be writing rules like A---B etc, and this game does not have any order or ranking component, you are correct in that regard.

You could think of this as a grouping game if that helps you, and that is likely what I would do here as well. Regardless of game type, your setup should look exactly like the above. Some companies would refer to this as a 3 way grouping game, but regardless of the name for it, the setup above is perfect, where the entities are being placed into different categories or groups.

I hope all this helps you, and I wish you all of the luck in your studies.

Best,
Ryan