A good general rule to keep in mind is that a single conditional rule will not cover all of the possible permutations; for instance, it won’t tell you that two variables must always be in the same group, or can never be in the same group. To get that level of certainty, you either need a second rule (a good example of this is the first game in Preptest 54, from June, 2008 – the first rule tells us that If Jaclyn is on stage, then Lorena is offstage, and the *second *rule tells us that if Lorena is offstage, then Jaclyn is onstage. Only after the second rule do we know that Jaclyn and Lorena must always be separated); OR, barring a second rule, we need an “if and only if” rule, which is really two rules in one single sentence. An example of this is from Preptest 56 (December 2008), the second game: “Grace helps most the sofa *if but only if* Heather moves the recliner. Now we know that they’re either both working on their respective pieces of furniture, or neither one of them is.

In these two games, if we know about Jaclyn, Lorena, Heather, or Grace, then we automatically know about the other person in their pairing, but it’s only because the rules gave us two pieces of information; if there’s only a single conditional rule, then there will always be ambiguous cases where a piece of information (like “Females are in V South”) doesn’t allow us to draw any further inferences.