Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The game scenario establishes that a company will make ordered deliveries of juices and snacks to four separate schools. The order of the deliveries (1, 2, 3, and 4) should be the base, and there should be rows for juices and snacks stacked above the base set. The schools (F, G, H, and I) are then a repeating variable set that fills each stack:

PT69_Game_#3_setup_diagram 1.png

With the basic structure in place, let’s examine each rule.

The first rule applies only to the snacks row, and establishes that F’s snack delivery is earlier than H’s snacks delivery. We’ll show the “snacks” reference with a subscript “S”:

PT69_Game_#3_setup_diagram 2.png

This rule creates two Not Laws, on the snacks row only:

PT69_Game_#3_setup_diagram 3.png

The F Not Law will play a role when evaluating the fourth rule, so we will return to this inference at that time.

The second rule creates a G Not Law on the fourth juices delivery, and the third rule establishes that G is the third snacks delivery:

PT69_Game_#3_setup_diagram 4.png

The fourth rule creates a direct connection between the first juices delivery and the fourth snacks delivery, which should be represented directly on the diagram for maximum visual effect:

PT69_Game_#3_setup_diagram 5.png

At first, this appears to be a fairly innocuous rule, but if you consider that any restriction on the first juices delivery or the fourth snacks delivery will limit the delivery options for both deliveries (which is why the arrow is a double-arrow), then the possible schools that can satisfy this rule are quickly reduced. For example, due to the effects of the first rule, F can never be the fourth snacks delivery. Thus, F also cannot be the first juices delivery. In addition, because G is the third snacks delivery according to the third rule, G cannot be the fourth snacks delivery, and therefore G cannot meet the requirements of the fourth rule. Thus, neither F nor G can be the delivery that is the first juices delivery and the fourth snacks delivery, leaving only H or I available to satisfy this rule:

PT69_Game_#3_setup_diagram 6.png

We can also infer that G must be the second or third juices delivery, because G cannot be the first juices delivery, and the second rule prohibits G from being the fourth juices delivery. In addition, we can infer that F must be the first or second snacks delivery, because F cannot be the fourth snacks delivery, and the third rule assigns G as the third snacks delivery. Adding these inferences to our diagram results in the final diagram:

PT69_Game_#3_setup_diagram 7.png

With the setup in hand, let’s move to the questions.