Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping Game, Defined-Moving, Balanced.

Although the number of variables in this game—sponsors in this case—being placed is defined at seven, the number of spaces per table is not precisely defined. This type of uncertainty almost always increases the difficulty of a game because it introduces another element that must be tracked during the game.

The first rule establishes that each table must have at least two sponsors seated at it, and since there are a total of seven sponsors, it can be deduced that one of the three tables will have three sponsors seated at it and the other two tables will each seat two sponsors. This 3-2-2 arrangement is known as a numerical distribution. In this case, the 3-2-2 distribution is “unfixed,” since the three sponsors could be seated at either table 1, table 2, or table 3. In some games “fixed” distributions occur, which is generally a benefit since this limits the possibilities within a game.

The other rules of the game are relatively straightforward, and your initial setup should appear similar to the following:

J97_Game_#1_setup_diagram 1.png

Since K, L, and M must sit at either table 1 or table 2, they cannot sit at table 3. Since V must sit at the same table as L, it follows that V cannot sit at table 3. Since K, L, M, and V cannot sit at table 3, only P, Q, and Z can possibly sit at table 3.
Clearly then, table 3 is extremely restricted. As in any game, always examine the points of restriction since they often yield powerful inferences. In this case, since table 3 must have at least two sponsors, and only P, Q, and Z can possibly sit at table 3, at least two of the P, Q, Z group must always sit at table 3. Therefore, if a question states that one of the P, Q,
Z group is seated at table 1 or table 2, then the remaining two sponsors must automatically be seated at table 3. Further, any arrangement that attempts to seat two of the P, Q, or Z group at table 1 or table 2 will violate the rules and thus cannot occur. Ultimately, this simple analysis has uncovered the most important inference of the game. To reiterate, since table 3 has only three available sponsors to fill at least two seats, if any one of the sponsors is seated elsewhere, the remaining two sponsors must be seated at table 3. This is a variation of the type of inferences common when a dual-option is present, and you can expect at least one or two of the questions to directly test your knowledge of this inference.

This game is very representative of the type of grouping games that frequently appear on the LSAT. There are two powerful lessons to learn from this game: First, always examine the restricted points in a game. In a grouping game this often means examining the available variables for a particular group, or examining the variables that cannot be placed together. Second, always examine any rule which deals with numbers. Often these numerical rules introduce a controlling factor into a game, such as a numerical distribution.