- PowerScore Staff
- Posts: 7871
- Joined: Feb 02, 2011
This is an Advanced Linear: Balanced, Identify the Templates game.
The game scenario establishes that each of three teachers will give one of six consecutive presentations, on six different subjects.
Because we are told which subject each teacher will present on, the two variable sets are not independent of each other. Given the “stacked” nature of our setup, we can use vertical blocks to represent the connection between the teachers and the subjects they present on:
With the basic structure in place, let us now turn to the rules.
The first rule establishes that K cannot give two presentations in a row:
Since we know which presentations are delivered by K, we can also represent this rule with three rotating Not-blocks:
The implications of this rule will be examined in greater detail later in our setup.
The second rule establishes the following relationship between S and O:
This rule creates an S Not Law, and an O Not Law:
The last rule establishes a similar relationship, this time between T and W:
This rule adds two more Not Laws to our diagram:
We can also add another Not Law under the Teacher row. Since W is the only subject that L can teach, then if W cannot be 1st, L cannot be 1st either. That leaves only two possibilities for the Teacher of the first subject:
With all three rules clearly diagrammed, it is critical to focus on the most restrictive rule in the game, which is the first rule. This is because K must present on three of the six subjects, and so the rule will affect at least half of the variables we are working with. Since K cannot give two presentations in a row, we must ensure that no two of these three variables are adjacent. The Separation Principle™ applies, requiring K to present in one of the following four ways:
1 - 3 - 5
1 - 3 - 6
1 - 4 - 6
2 - 4 - 6
You should notice that in three of these scenarios, K delivers the sixth presentation, which cannot be S or T. Therefore, if K delivers the sixth presentation, that presentation must be P:
Thus, we arrive at the final setup for this game:
Due to the incredibly restrictive effect of the Separation Principle™ produced by the last rule, it is worth creating four templates to represent the ways in which K gives the three presentations. our task is also facilitated by the fact that two of K’s presentations—S and T—are each subject to a sequencing rule involving O and W, respectively.
Given the second and third rules (S O and T W, respectively), we can also infer that the fifth presentation in Template 3 must be either O or W. The same is true about the third and fifth presentations in Template 4, forcing N to be the first presentation in that template:
With these four templates in place, attacking the questions will be relatively straightforward.