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This is an Advanced Linear Game: Balanced.
The diagram to this game is quite powerful since most of the spaces can be filled in.
From the game scenario, we know that there are three variable sets: the seven tracks, the seven songs, and the two types (new and rock classic). Because the seven tracks have a numerical order, they are the better choice for the base. This choice creates a linear setup with two stacks, one for the songs and one for the types (remember to leave ample vertical space between the two stacks since each row will likely have its own Not Laws):
Because the rules have so many consequences, let’s examine each rule:
Rule #1. This is the most straightforward rule of the game, and it can be represented by placing an “S” in fourth space of the Song row:
Rule #2. This rule states that both W and Y precede S on the CD, and this rule can be diagrammed as:
By itself, this rule means that W and Y cannot be tracks 5, 6, or 7 on the CD (because the first rule establishes that S is 4th)
Rule #3. This rule can be diagrammed as:
- T W
This sequence indicates that T, W, and Y must all precede S on the CD. Of course, if T, W, and Y precede S, they occupy the first three spaces, and that leaves only spaces 5, 6, and 7 for V, X, and Z:
Thus, although all songs have not been specifically placed, we do know how they are divided on either side of S. Also, because T must precede W, we can ascertain that W cannot be first and T cannot be third.
Rule #4. This rule specifies that the sixth track is a rock classic. This information can be added directly to the diagram:
Rule #5. This rule can be diagrammed as:
Note that this rule only applies to rock classics. A new song does not have to be followed by a rock classic.
The appearance of this rule creates several inferences. First, because a rock classic must be preceded by a new song, the first song on the CD must be a new song (a rock classic cannot be first because then it would not be preceded by a new song). Second, because the sixth song is a rock classic, we can automatically determine that the fifth song must be a new song. Third, because the sixth song is a rock classic, the seventh song must be a new song (if the seventh song was a rock classic, then the sixth song would have to be a new song). Adding this information creates the following setup:
Rule #6. This rule states that Z is a rock classic. When considered with the fifth rule, this rule can be diagrammed as follows:
However, we already know from the analysis in rule #3 that Z must be the fifth, sixth, or seventh song on the CD. And, since the analysis in rule #5 indicated that, of those three tracks, only the sixth track could be a rock classic, we can determine that Z must be the sixth track on the CD. Accordingly, V and X must occupy the fifth and seventh tracks, not necessarily in that order:
Compiling all of the information above, we arrive at the final setup for this game: