Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination Game.

This Grouping/Linear combination game features eight lectures filling six spaces, and thus whenever two lectures are eliminated from the scheduling, the remaining six lectures must be scheduled. Questions #16 and #17 are excellent examples of this principle in action. The morning and afternoon variable sets also add an advanced linear element to the game, and consequently the game is difficult. The setup to the game is as follows:

Dec 94_M12_game#3_L7_explanations_game#1_setup_diagram_1.png

Since the three days contain an inherent sense of order, they are chosen as the base and the morning and afternoon variable sets are stacked on top. “Morning” and “afternoon” have been abbreviated as AM and PM because they are too time-consuming to write out. It makes no difference whether your diagram has the AM set as the top row or as the bottom row.

Because of the vertical component, the OL and PL rules are written in block form. For convenience L has been placed on the bottom in both rules, but it is essential to understand that O and L (and P and L) can never be scheduled for the same day, regardless of which one is in the AM or PM. If this confuses you, each rule can be written out both ways for clarity:

Dec 94_M12_game#3_L7_explanations_game#1_setup_diagram_2.png

Note also that the first rule has not been written out. Instead of showing that O could go on day 2 (O should not be placed on day 2 on the diagram because we cannot be sure O is one of the six scheduled lectures), it is preferable to show that O cannot go on day 1 and day 3. Superior representations always reflect the absolutes—what must occur and what cannot occur. In examining the diagram it is also important to note that the O Not Laws on day 1 and day 3 apply to both the AM and PM. They can be placed on each row for each day if you feel that is necessary.

The last rule is difficult to diagram concisely. There are two scenarios under the rule: when P is scheduled for day 1, then F and H are scheduled for day 2, and when P is scheduled for day 2 then F and H are scheduled for day 3. In the form we have chosen, we have combined the two possibilities and represented them through the “1, 2” and “2, 3” subscripts. If you find this confusing, write out each scenario separately. This rule is especially important because it needs a lot of space. Also, do not forget to take the contrapositive of the rule: if any variable other than F or H is scheduled for day 2, then P cannot be scheduled for day 1, and if any variable other than F or H is scheduled for day 3, then P cannot be scheduled for day 2. This important inference is tested.

Because each appears in two rules, O and P are the key variables in the game and you must always be aware of them. In contrast to O and P, N is a random and relatively weak variable. Remember that in games with a large number of variables—say 9 or 10—randoms are relatively weak, and that in games with few variables—5 or 6—randoms are stronger and need to be given more consideration.

Finally, it is notable that this game does not contain any extremely deep inferences. There are some obvious inferences—for example, if L is scheduled for day 2, then O cannot be scheduled at all—but nothing truly challenging. This may in part explain why five of the six questions are local: to create challenging situations the test makers had to supply local conditions to create limitation. Some games with deep inferences or limited possibilities have a large number of global questions to test your knowledge of the inferences. The first game from the June 1999 LSAT is a good example (only several possibilities exist and consequently all five questions are global).