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#40612
Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

The game scenario establishes that seven manuscripts were written at seven different times:
PT69_Game_#1_setup_diagram 1.png
This creates a Basic Linear diagram, and because there are seven variables for seven positions, this is a Balanced game. With the basic structure in place, let us now turn to the rules.

The first rule creates the following sequence:
  • ..... ..... ..... ..... ..... ..... F :longline: H :longline: S
This sequence creates six Not Laws on the diagram:
PT69_Game_#1_setup_diagram 2.png
The second rule creates a simple block:
PT69_Game_#1_setup_diagram 3.png
This block adds two more Not Laws to the diagram:
PT69_Game_#1_setup_diagram 4.png
The third and fourth rules are similar: L is eliminated from the first four spaces, and M is eliminated from the last four spaces, adding eight more Not Laws:
PT69_Game_#1_setup_diagram 5.png
Note that the first and seventh positions have four of the seven manuscripts eliminated, leaving triple options on each (F/G/M on first, and L/P/S on seventh; these will be shown on the next diagram).

The diagrammatic representation for the third and fourth rules varies depending on preference. Represented off to the side of the diagram, the rules would appear as:
PT69_Game_#1_setup_diagram 6.png
Because that results in a limited selection of spots for L and M, a better approach is to simply represent the two rules on the diagram:
PT69_Game_#1_setup_diagram 7.png
The fifth rule adds an H Not Law on 5:
PT69_Game_#1_setup_diagram 8.png
Rules like this one can feel minor or inconsequential (especially in comparison to the four prior rules), but LSAC loves to throw in a rule that looks like an afterthought, and then not use that rule until the very end of the game (when, presumably, most test takers have forgotten about the rule). That turns out to be the case with this rule, which doesn’t play a major role until the last question of the game.

At this point, each of the rules has been represented, and appropriate Not Laws drawn. Let’s now look at some inferences. The first inference comes from linking the first and last rules. Because H appears in each rule, we should examine the action of the
F :longline: H :longline: S sequence around the fifth position. Most notably, we can infer that if F is written fourth, then H and S must be written sixth and seventh, respectively:
PT69_Game_#1_setup_diagram 9.png
Next, consider that in this game there is a 3-variable sequence, a 2-variable block, and severe limitations on the placement of two variables (L and M). Further, there is no overlap between the variables in those elements, so one can deduce that there must be some restrictions in the movements of certain variables. Let’s examine the F :longline: H :longline: S sequence as it relates to L and M.

The rule restrictions on L and M limit each to just three spaces, the last three spots in the case of L, and the first three spots in the case of M. The F :longline: H :longline: S sequence also requires three spaces (albeit not consecutive spaces), and the convergence of these two elements creates two inferences:
  • If F was written fifth, then H and S would have to have been written sixth and seventh, respectively. However, this alignment fully occupies the fifth, sixth, and seventh positions completely, leaving no room for L. Thus, F cannot have been written fifth.

    If S was written third, then F and H would have to have been written first and second, respectively. However, this alignment fully occupies the first, second, and third positions completely, leaving no room for M. Thus, S cannot have been written third.
When these two not Laws are added to the diagram, we arrive at the final setup for the game:
PT69_Game_#1_setup_diagram 10.png
There are more inferences in this game—question #4 makes that apparent—but figuring out that inference while under time pressure is exceptionally difficult, and so we’ll examine that inference when we arrive at question #4.

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