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This is a Defined-Moving, Balanced Grouping game.
At first glance, this Game appears to be Undefined because it is not immediately clear how the seven variables will be divided into the two groups, F and I. However, the third and fourth rules establish conditions that serve to restrict the distribution possibilities to a high degree (as will be discussed momentarily), thus this Game can be considered largely Defined.
Another important point to consider when attacking this Game is the two-value system. Because there are two committees here—Finance and Incentives—and the board members must each be placed into exactly one of the two committees, you can make powerful inferences when you determine both where a person must go, as well as when you determine where a person cannot go. That is, if a member cannot be on the finance committee, you can infer that that member must be on the incentives committee. This idea will also come into play as we take contrapositives of the conditional rules for this Game.
Finally, because each of the five rules is purely conditional, this Game can be described as a Pure Grouping Game. In Pure Grouping games you are generally not able to make definitive inferences about where variables must be placed, but rather you must understand the relationships between certain variables and how they may or may not be grouped with one another. So we will not be able to make a diagram in the traditional sense; we cannot create a group of say, five spaces and then place variables in those spaces. Instead, we must diagram the rules and make inferences, and then proceed to the questions without a set group in place. Some similar games (albeit less defined) are: October 2005 #2 (Light Switches), December 2005 #1 (Electrical Appliances), and June 2006 #3 (Summer Courses).
G H L M U W Z 7
- GF HI
- LF MI + UI
MF or UF LI
- W Z
- U G
- ZF HF
There are four main inferences (chains of inferences) that result from a combination of two or more of the rules listed previously.
You know that if G is in F, then H is in I (first rule), and you also know that if H is in I, then Z is in I (last rule). Further, you know that G and U cannot be together, so if G is in F, then U must be in I. This creates:
- GF HI + UI + ZI
You know that if H is in F, then G is in I (rule 1), and you know that G and U are not together (rule 4) so G in I would place U in F. You also know that if U is in F then L is in I (rule 2), so you have the following:
- HF GI + UF + LI
You are told that Z in F means that H is in F (rule 5), and H in F indicates something about G, U, and L (Inference 2 above). Further, since Z and W must be separated (rule 3), then Z in F would place W in I. This yields:
- ZF HF + GI + UF + LI + WI
You know that H in I tells you that Z is also in I (rule 5), and you know that Z and W must be separated. This produces:
- HI ZI + WF